user88: I have heard that mining is for people with ready hardware and blah blah blah... But what exactly is it? Does it operate like real mining? I mean, people talk about it like you are physically mining.

user4020: The answers in this section all present different, useful perspectives.  Another useful, but non-technical perspective is:
Mining is a battle between those who want to see Bitcoin succeed for the greater good, and those who don't care if it is destroyed as long as they achieve some victory, even if only to be part of the destruction (they might not get any BTCs from their destructive efforts).
In other words, Bitcoin is a fascinating attempt to establish an alternate money system.  Since the P2P, decentralised architecture is integral to its success it is, by design, open to any participant.  The mining process assumes that some participants are evil.  It pitches 'good' against 'evil' in the hope that 'good' will continue to succeed and maintain the integrity of the network.

user11969: In more simple terms:
Actual mining means, you sweat digging something and then find some useful metals.
In bitcoin mining, your computer sweats calculating blocks and in return the bitcoin protocol gives you some bitcoins.
And in actual mining, you find precious metals which doesn't belong to anyone. Similarly, in bitcoin mining, the bitcoin protocol generates new bitcoins (Only upto 21 millions though) (which are not belonged to anybody) and gives you.
So the word "mining" makes perfect sense.

user78: Mining is just doing computational work to secure the transaction block chain. A side effect of mining is creation of new coins and earning additional money by signing on transactions.

user85: Mining is the process of securing transactions and committing them into the bitcoin public chain. It requires winning a kind of computational lottery where each hash you perform is like buying one ticket. The Bitcoin protocol currently permits the miner who generates a block to claim 50 bitcoins as well as any transaction fees for the transactions that miner chooses to include.
The Bitcoin system uses the mining process to generate coins, secure transactions, and publish transactions.

user365: mining is doing the work of finding nonce so that sha256(sha256(data+nonce)) < difficulty
where

nonce is an integer number the miner chooses freely (this choosing of the nonce and checking if the condition (< difficulty) is met comprises the work
data is a hash over the contents of the block (transactions) and the previous block's hash
sha256() is the SHA-256 cryptographic hashing function (wikpedia SHA-2 article)
difficulty is a value that is adjusted consensually by the nodes of the bitcoin network to adjust for change in network computation power in order to have one block every 10 minutes found by the network

The resulting nonce is the proof of work: since it's impossible to find nonce without essentially trying different nonces and calculating the two hash functions, having found a nonce that satisfies the condition is proof this work of searching and calculating has in fact been done. 
This is the central idea behind Bitcoin to solve the double spending problem: due to the inclusion of the previous block's hash in data (this links the blocks to form a chain) and the fact that the honest nodes of the network always do their work on the longest chain of blocks, a double spending attack involves calculating (and later publishing) a forked block chain in secret that is longer than the "honest chain" (containing the transaction that should be undone). 
Due to the work required to do this, this race can only be won if the attacker has greater computation power than the rest of the network together. Since using such computation power to honestly mine is likely more profitable than pulling a double-spend, the incentive for doing a double-spend attack is low.

user44: David Schwartz's answer is entirely accurate, but all that "bitspeak" might be a little intimidating to the average user.  Let me try and put it into more plain language:
The way Bitcoin works is that instead of having one central authority who secures and controls the money supply (like most governments do for their national currencies), this work is spread out all across the network.  Most of the heavy lifting for Bitcoin is done by "miners".
Miners collect the transactions on the network (like "Alice pays Karim 10 bitcoins" and "Liam pays Sofia 8.3 bitcoins") into large bundles called blocks.  These blocks are strung together into one continuous, authoritative record called the block chain, which doesn't permit any conflicting transactions.  This is necessary because without it people would be able to sign the same bitcoins over to two different recipients, like writing cheques for more money than you have in your account.  The block chain lets you know for sure exactly which transactions count and can be trusted (so no bad cheques!).
The way Bitcoin makes sure there is only one block chain is by making blocks really hard to produce.  So instead of just being able to make blocks at will, miners have to compute a cryptographic hash of the block that meets certain criteria.  Bitcoiners refer to this process as "hashing".  The only way to find a cryptographic hash that's "good enough to count" is to try computing a whole bunch of them until you get lucky and find one that works.  This is the "lottery" that David Schwartz refers to, because miners who successfully create a block are rewarded some bitcoins according to a preset schedule.  The difficulty of the criteria for the hash is continually adjusted based on how frequently blocks are appearing, so more competition equals more work needed to find a block.  Modern dedicated mining hardware (e.g. ASIC miners) can try trillions of hashes per second, so to be competitive in this race to find hashes miners need specialised hardware, otherwise they will tend to spend more on electricity than they make in the "lottery".
In addition to the hash criteria, a block needs to contain only valid, non-conflicting transactions.  So the other main task for miners is to carefully validate all the transactions that go into their blocks, otherwise they won't get any reward for their work!
Because of all this work, when a Bitcoin client signs on to the network it can trust the block chain that was most difficult to produce (since this is evidently the one that was being worked on by the most miners).  If there was a "fake" blockchain competing with the real ones (say, where someone pretends that they didn't actually give Sofia those 8.4 bitcoins and they still have them), the fraudster would have to do as much work as the whole rest of the network to make their block chain look as trustworthy.  So essentially, the intense work that goes into finding blocks through hashing secures the network against fraud.  There is also, of course, some nifty code that figures out how to choose between conflicting transactions; and what to do if two people find valid blocks at the same time.
One last thing:  why is it called mining?  In the original analogy, people who performed this essential work were compared to gold miners digging the gold out of the ground so that everyone could use it.  But in reality, Bitcoin "miners" are just running computer programs on very specialised hardware that automates the process of securing the network.  To sum up, this software

Collects transactions from the network
Validates them, and doesn't allow conflicting ones
Puts them into large bundles called blocks
Computes cryptographic hashes over and over until if finds one "good enough to count"
Then submits the block to the network, adding it to the block chain and earning a reward in return.

That's mining in a nutshell!

88: <p>I have heard that mining is for people with ready hardware and blah blah blah... But what exactly is it? Does it operate like real mining? I mean, people talk about it like you are <em>physically</em> mining.</p>
 4020: <p>The answers in this section all present different, useful perspectives.  Another useful, but non-technical perspective is:</p>

<p>Mining is a battle between those who want to see Bitcoin succeed for the greater good, and those who don't care if it is destroyed as long as they achieve some victory, even if only to be part of the destruction (they might not get any BTCs from their destructive efforts).</p>

<p>In other words, Bitcoin is a fascinating attempt to establish an alternate money system.  Since the P2P, decentralised architecture is integral to its success it is, by design, open to any participant.  The mining process assumes that some participants are evil.  It pitches 'good' against 'evil' in the hope that 'good' will continue to succeed and maintain the integrity of the network.</p>
 11969: <p>In more simple terms:
Actual mining means, you sweat digging something and then find some useful metals.
In bitcoin mining, your computer sweats calculating blocks and in return the bitcoin protocol gives you some bitcoins.</p>

<p>And in actual mining, you find precious metals which doesn't belong to anyone. Similarly, in bitcoin mining, the bitcoin protocol generates new bitcoins (Only upto 21 millions though) (which are not belonged to anybody) and gives you.</p>

<p>So the word "mining" makes perfect sense.</p>
 78: <p><a href="https://en.bitcoin.it/wiki/How_bitcoin_works#Bitcoin_mining">Mining</a> is just doing computational work to secure the transaction block chain. A side effect of mining is creation of new coins and earning additional money by signing on transactions.</p>
 85: <p>Mining is the process of securing transactions and committing them into the bitcoin public chain. It requires winning a kind of computational lottery where each hash you perform is like buying one ticket. The Bitcoin protocol currently permits the miner who generates a block to claim 50 bitcoins as well as any transaction fees for the transactions that miner chooses to include.</p>

<p>The Bitcoin system uses the mining process to generate coins, secure transactions, and publish transactions.</p>
 365: <p><strong><em>mining</em> is doing the <em>work</em> of finding <em>nonce</em> so that <em>sha256(sha256(data+nonce)) &lt; difficulty</em></strong></p>

<p>where</p>

<ul>
<li><em>nonce</em> is an integer number the miner chooses freely (this choosing of the nonce and checking if the condition (<em>&lt; difficulty</em>) is met comprises the <em>work</em></li>
<li><em>data</em> is a hash over the contents of the block (transactions) and the previous block's hash</li>
<li><em>sha256()</em> is the SHA-256 cryptographic hashing function (<a href="http://en.wikipedia.org/wiki/SHA-2">wikpedia SHA-2 article</a>)</li>
<li><em>difficulty</em> is a value that is adjusted consensually by the nodes of the bitcoin network to adjust for change in network computation power in order to have one block every 10 minutes found by the network</li>
</ul>

<p>The resulting <em>nonce</em> is the <em>proof of work</em>: since it's impossible to find <em>nonce</em> without essentially trying different <em>nonces</em> and calculating the two hash functions, having found a <em>nonce</em> that satisfies the condition is proof this <em>work</em> of searching and calculating has in fact been done. </p>

<p>This is the central idea behind Bitcoin to solve the double spending problem: due to the inclusion of the previous block's hash in <em>data</em> (this links the blocks to form a chain) and the fact that the honest nodes of the network always do their <em>work</em> on the longest chain of blocks, a <a href="http://en.wikipedia.org/wiki/Double-spending">double spending</a> attack involves calculating (and later publishing) a forked block chain in secret that is longer than the "honest chain" (containing the transaction that should be undone). 
Due to the <em>work</em> required to do this, this race can only be won if the attacker has greater computation power than the rest of the network together. Since using such computation power to honestly mine is likely more profitable than pulling a double-spend, the incentive for doing a double-spend attack is low.</p>
 44: <p>David Schwartz's answer is entirely accurate, but all that "bitspeak" might be a little intimidating to the average user.  Let me try and put it into more plain language:</p>

<p>The way Bitcoin works is that instead of having one central authority who secures and controls the money supply (like most governments do for their national currencies), this work is spread out all across the network.  <strong>Most of the heavy lifting for Bitcoin is done by "miners".</strong></p>

<p>Miners collect the transactions on the network (like "Alice pays Karim 10 bitcoins" and "Liam pays Sofia 8.3 bitcoins") into large bundles called <strong><a href="https://en.bitcoin.it/wiki/Block" rel="noreferrer">blocks</a></strong>.  These blocks are strung together into one continuous, authoritative record called the <strong><a href="https://en.bitcoin.it/wiki/Block_chain" rel="noreferrer">block chain</a></strong>, which doesn't permit any conflicting transactions.  This is necessary because without it people would be able to sign the same bitcoins over to <a href="http://en.wikipedia.org/wiki/Double-spending" rel="noreferrer">two different recipients</a>, like writing cheques for more money than you have in your account.  <strong>The block chain lets you know for sure exactly which transactions count and can be trusted</strong> (so no bad cheques!).</p>

<p>The way Bitcoin makes sure there is only one block chain is by making blocks really hard to produce.  So instead of just being able to make blocks at will, miners have to compute a <a href="http://en.wikipedia.org/wiki/Cryptographic_hash_function" rel="noreferrer">cryptographic hash</a> of the block that meets certain criteria.  Bitcoiners refer to this process as <strong>"hashing"</strong>.  The only way to find a cryptographic hash that's "good enough to count" is to try computing a whole bunch of them until you get lucky and find one that works.  This is the "lottery" that David Schwartz refers to, because miners who successfully create a block are <a href="https://bitcoin.stackexchange.com/questions/161/how-many-bitcoins-will-there-eventually-be">rewarded some bitcoins according to a preset schedule</a>.  The difficulty of the criteria for the hash is continually adjusted based on how frequently blocks are appearing, so <strong>more competition equals more work needed to find a block</strong>.  Modern dedicated mining hardware (e.g. ASIC miners) can try trillions of hashes per second, so to be competitive in this race to find hashes miners need specialised hardware, otherwise they will tend to spend more on electricity than they make in the "lottery".</p>

<p>In addition to the hash criteria, a block needs to contain only valid, non-conflicting transactions.  So <strong>the other main task for miners is to carefully validate all the transactions that go into their blocks</strong>, otherwise they won't get any reward for their work!</p>

<p>Because of all this work, when a Bitcoin client signs on to the network it can trust the block chain that was most difficult to produce (since this is evidently the one that was being worked on by the most miners).  If there was a "fake" blockchain competing with the real ones (say, where someone pretends that they didn't <em>actually</em> give Sofia those 8.4 bitcoins and they still have them), the fraudster would have to do as much work as the whole rest of the network to make their block chain look as trustworthy.  So essentially, <strong>the intense work that goes into finding blocks through hashing secures the network against fraud</strong>.  There is also, of course, some nifty code that figures out how to choose between conflicting transactions; and what to do if two people find valid blocks at the same time.</p>

<p>One last thing:  <strong>why is it called mining?</strong>  In the original analogy, people who performed this essential work were compared to gold miners digging the gold out of the ground so that everyone could use it.  But in reality, Bitcoin "miners" are just running computer programs on very specialised hardware that automates the process of securing the network.  To sum up, this software</p>

<ul>
<li><strong>Collects transactions from the network</strong></li>
<li><strong>Validates them, and doesn't allow conflicting ones</strong></li>
<li><strong>Puts them into large bundles called <a href="https://en.bitcoin.it/wiki/Block" rel="noreferrer">blocks</a></strong></li>
<li><strong>Computes <a href="http://en.wikipedia.org/wiki/Cryptographic_hash_function" rel="noreferrer">cryptographic hashes</a> over and over until if finds one "good enough to count"</strong></li>
<li><strong>Then submits the block to the network, adding it to the block chain and earning a reward in return</strong>.</li>
</ul>

<p><strong>That's mining in a nutshell!</strong></p>
