user1377: I searched the bitcoin wiki and found references to coinbase, but no clear cut explanation of what exactly it is.  I know that miners can tag their coinbases (that is how some sites tell who mined a block).

user5406: David has already given a good explanation of the term coinbase, but I'd like to give further details on the coinbase transaction.
The coinbase transaction is a special type of transaction. 

Every block must have a coinbase transaction, other transactions are optional.
The coinbase transaction must be the first transaction of the block (it follows that there can only be one per block).
The coinbase's output is used to send the block reward, i.e. block subsidy plus transaction fees, to the miner's address.
The coinbase transaction can have an arbitrary input of 100 byte size. E.g. this was where the genesis block famously contained "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks". This is also the field that may be used for the extranonce.


user85: The term "coinbase" is used to mean many different things. But the two you're probably asking about are:

The "coinbase transaction" is the transaction inside a block that pays the miner his block reward.
Inside the coinbase transaction is a field that is called the "coinbase". It's the generation transaction's equivalent of a scriptsig. Since it doesn't claim any existing outputs, it needs no normal scriptsig. It's basically just a random value that the miner can use as an additional nonce. BIP 34 changes this a bit.


1377: <p>I searched the bitcoin wiki and found references to coinbase, but no clear cut explanation of what exactly it is.  I know that miners can tag their coinbases (that is how some sites tell who mined a block).</p>
 5406: <p>David has already given a good explanation of the term coinbase, but I'd like to give further details on the <strong>coinbase transaction</strong>.</p>

<p>The <em>coinbase transaction</em> is a special type of transaction. </p>

<ul>
<li>Every block must have a coinbase transaction, <a href="https://bitcoin.stackexchange.com/q/2021/5406">other transactions are optional</a>.</li>
<li>The coinbase transaction must be the first transaction of the block (it follows that there can only be one per block).</li>
<li>The coinbase's output is used to send the block reward, i.e. block subsidy plus transaction fees, to the miner's address.</li>
<li>The coinbase transaction can have an arbitrary input of 100 byte size. E.g. this was where the genesis block famously contained "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks". This is also the field that may be used for the <a href="https://bitcoin.stackexchange.com/q/5048/5406"><code>extranonce</code></a>.</li>
</ul>
 85: <p>The term "coinbase" is used to mean many different things. But the two you're probably asking about are:</p>

<ol>
<li><p>The "coinbase transaction" is the transaction inside a block that pays the miner his block reward.</p></li>
<li><p>Inside the coinbase transaction is a field that is called the "coinbase". It's the <a href="https://en.bitcoin.it/wiki/Transactions#Generation">generation transaction's</a> equivalent of a scriptsig. Since it doesn't claim any existing outputs, it needs no normal scriptsig. It's basically just a random value that the miner can use as an additional nonce. <a href="https://en.bitcoin.it/wiki/BIP_0034">BIP 34</a> changes this a bit.</p></li>
</ol>
