user97892: Here is what I've understood of bitcoin:

Everybody has a public and private key.
If A sends bitcoins to B:


B is generating an address and sends it to A
This addresses are generated for each transaction.
A needs to sign something with his private key and B's address


Am I wrong?
If not, I want to understand how this address is computed.
I have read it is a kind of public key computed from private key. That's it? So we can have many public keys which match to a common private key?
I have also read the address is derived from the public key.

user101498: 
Everybody has a public and private key.

Everybody is able to generate any number of private keys ("randomly") and derive a public key from it.

If A sends bitcoins to B:
B is generating an address and sends it to A

B forms an address out of the public key itself derived from a "randomly" generated private key.

This addresses are generated for each transaction.

Ideally yes, unfortunately (privacy-wise) it's a decision made by the sender. Sending twice to the same address is possible.

A need to sign something with his private key and B's address

This something is, basically, the transaction itself.
EDIT: To answer the question title :-)

What is physically an address in bitcoin

Some bytes either stored on your hard disk or in memory, which are part of a transaction and which are to be interpreted as a script describing what conditions should be met to spend the coins "next to" this address.

97892: <p>Here is what I've understood of bitcoin:</p>

<ul>
<li>Everybody has a public and private key.</li>
<li>If A sends bitcoins to B:

<ul>
<li>B is generating an address and sends it to A</li>
<li>This addresses are generated for each transaction.</li>
<li>A needs to sign something with his private key and B's address</li>
</ul></li>
</ul>

<p>Am I wrong?</p>

<p>If not, I want to understand how this address is computed.</p>

<p>I have read it is a kind of public key computed from private key. That's it? So we can have many public keys which match to a common private key?
I have also read the address is derived from the public key.</p>
 101498: <blockquote>
<p>Everybody has a public and private key.</p>
</blockquote>
<p>Everybody is able to generate any number of private keys (&quot;<a href="https://en.wikipedia.org/wiki/CSPRNG" rel="nofollow noreferrer">randomly</a>&quot;) and derive a public key from it.</p>
<blockquote>
<p>If A sends bitcoins to B:</p>
<p>B is generating an address and sends it to A</p>
</blockquote>
<p>B <em><a href="https://en.bitcoin.it/wiki/Address" rel="nofollow noreferrer">forms</a></em> an address out of the public key itself derived from a &quot;randomly&quot; generated private key.</p>
<blockquote>
<p>This addresses are generated for each transaction.</p>
</blockquote>
<p>Ideally yes, unfortunately (privacy-wise) it's a decision made by the sender. Sending twice to the same address is possible.</p>
<blockquote>
<p>A need to sign something with his private key and B's address</p>
</blockquote>
<p>This something is, <em><a href="https://en.bitcoin.it/wiki/OP_CHECKSIG" rel="nofollow noreferrer">basically</a></em>, the transaction itself.</p>
<p>EDIT: To answer the question title :-)</p>
<blockquote>
<p>What is physically an address in bitcoin</p>
</blockquote>
<p>Some bytes either stored on your hard disk or in memory, which are part of a <a href="https://en.bitcoin.it/wiki/Transaction" rel="nofollow noreferrer">transaction</a> and which are to be interpreted as a <a href="https://en.bitcoin.it/wiki/Script" rel="nofollow noreferrer">script</a> describing what conditions should be met to spend the coins &quot;<a href="https://en.bitcoin.it/wiki/Protocol_documentation#tx" rel="nofollow noreferrer">next to</a>&quot; this address.</p>
