user5406: What is a wallet in the context of Bitcoin? 
What are wallets used for? 
What relation do wallets have to other concepts such as addresses, private-keys, client-software, and Bitcoin balances?

user4334: A wallet is a collection of private keys used for un-encumbering UTXOs. From the intro of "Chapter 4. Keys, Addresses, Wallets" of Mastering Bitcoin:

Ownership of bitcoin is established through digital keys, bitcoin addresses, and digital signatures. The digital keys are not actually stored in the network, but are instead created and stored by users in a file, or simple database, called a wallet. The digital keys in a user’s wallet are completely independent of the bitcoin protocol and can be generated and managed by the user’s wallet software without reference to the blockchain or access to the Internet. Keys enable many of the interesting properties of bitcoin, including de-centralized trust and control, ownership attestation, and the cryptographic-proof security model.

"Type-0 nondeterministic (random) wallet" (each "k" is a randomly-generated key):

"Type-2 hierarchical deterministic [HD] wallet: a tree of keys generated from a single seed":


user60358: There is no official definition for a bitcoin wallet. Typically it is any of:

A graphical app for core tasks like: key (re)generation/import and performing blockchain transactions. 
A database consisting of one or more keys and/or seeds.  
A combination of the above. 

A seed or 'master key' can be used to (re)generate a set of keys. A set of keys is sometimes also called a keyring.

Since the metaphor should emphasize "something used to protect and hold together the things of value" a single key could also be compared to a wallet, as it can hold multiple UTXOs together. 
The fact that paper wallet is a common term means that the software is often not considered to be an integral part of a 'wallet'. Yet in the digital contexts it is common to 'install a wallet' and generate a keyring, implying the opposite: that the keys are not integral to the wallet and they can be transferred between wallets. 
This apparent inconsistency is explained by the realization that the 'wallet' metaphor is very flexible and applicable to multiple scenarios of bitcoin management. In short, "wallet" is overloaded and can mean several things in the context of bitcoin.

user26877: Bitcoin is like digital cash.
A bitcoin address is like an email account but for cash. 
A bitcoin address has a private key and a public key.
The public key is like your email (joesmith@gmail.com)
The private key is like your password to access your email (mypassword)
The main difference here is that a bitcoin private key holds all the information to access the account. So with a private key you can get the public key. 
A bitcoin wallet holds the private keys to bitcoin addresses - so instead of a wallet, think of it as a key chain with keys to different safes.
Wallets are used as an interface where you can access the bitcoins in your addresses without having to enter the private key in each time.
It makes the user experience a lot easier. So instead of entering in your private key each time you just might enter in a pin code instead.
Wallets also let you easily see the balance of each address, add and remove accounts (addresses) and send and receive bitcoin.
This is a very basic explanation but a good one to start with.
Hope this helps.

5406: <p>What is a <strong>wallet</strong> in the context of Bitcoin? </p>

<p>What are wallets used for? 
What relation do wallets have to other concepts such as addresses, private-keys, client-software, and Bitcoin balances?</p>
 4334: <p>A wallet is a collection of private keys used for un-encumbering UTXOs. From the intro of "<a href="http://chimera.labs.oreilly.com/books/1234000001802/ch04.html" rel="nofollow noreferrer">Chapter 4. Keys, Addresses, Wallets</a>" of <em><a href="http://chimera.labs.oreilly.com/books/1234000001802/index.html" rel="nofollow noreferrer">Mastering Bitcoin</a></em>:</p>

<blockquote>
  <p>Ownership of bitcoin is established through <em>digital keys</em>, <em>bitcoin addresses</em>, and <em>digital signatures</em>. The digital keys are not actually stored in the network, but are instead created and stored by users in a file, or simple database, called a <em><strong>wallet</strong></em>. The digital keys in a user’s wallet are completely independent of the bitcoin protocol and can be generated and managed by the user’s wallet software without reference to the blockchain or access to the Internet. Keys enable many of the interesting properties of bitcoin, including de-centralized trust and control, ownership attestation, and the cryptographic-proof security model.</p>
</blockquote>

<p>"Type-0 nondeterministic (random) wallet" (each "k" is a randomly-generated key):
<a href="https://i.stack.imgur.com/vBdqU.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/vBdqU.png" alt="Type-0 wallet"></a></p>

<p>"Type-2 hierarchical deterministic [HD] wallet: a tree of keys generated from a single seed":
<a href="https://i.stack.imgur.com/AvjAF.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/AvjAF.png" alt="Type-2 wallet"></a></p>
 60358: <p>There is no official definition for a bitcoin wallet. Typically it is any of:</p>

<ul>
<li>A graphical <strong>app</strong> for core tasks like: key (re)generation/import and performing blockchain transactions. </li>
<li>A <strong>database</strong> consisting of one or more keys and/or seeds.  </li>
<li>A combination of the above. </li>
</ul>

<p>A seed or 'master key' can be used to (re)generate a set of keys. A set of keys is sometimes also called a keyring.</p>

<hr>

<p>Since the metaphor should emphasize "something used to protect and hold together the things of value" a single key could also be compared to a wallet, as it can hold multiple UTXOs together. </p>

<p>The fact that paper wallet is a common term means that the software is often not considered to be an integral part of a 'wallet'. Yet in the digital contexts it is common to 'install a wallet' and generate a keyring, implying the opposite: that the keys are not integral to the wallet and they can be transferred between wallets. </p>

<p>This apparent inconsistency is explained by the realization that the 'wallet' metaphor is very flexible and applicable to multiple scenarios of bitcoin management. In short, "wallet" is overloaded and can mean several things in the context of bitcoin.</p>
 26877: <p>Bitcoin is like digital cash.
A bitcoin address is like an email account but for cash. 
A bitcoin address has a private key and a public key.
The public key is like your email (joesmith@gmail.com)
The private key is like your password to access your email (<strong><em>mypassword</em></strong>)
The main difference here is that a bitcoin private key holds all the information to access the account. So with a private key you can get the public key. </p>

<p>A bitcoin wallet holds the private keys to bitcoin addresses - so instead of a wallet, think of it as a key chain with keys to different safes.
Wallets are used as an interface where you can access the bitcoins in your addresses without having to enter the private key in each time.
It makes the user experience a lot easier. So instead of entering in your private key each time you just might enter in a pin code instead.
Wallets also let you easily see the balance of each address, add and remove accounts (addresses) and send and receive bitcoin.
This is a very basic explanation but a good one to start with.
Hope this helps.</p>
