An atheist does not believe in the existence of a deity, for the reason that there is no proof for its existence. This is in line with scientific enquiry, and is the rational position to take. An agnostic is not committed either way to the belief or disbelief of a deity. An agnostic may therefore believe that a deity may or may not exist, but simply not be fully committed.
Atheists often define themselves as agnostics because of the prejudices that often surround atheism. Agnosticism is often regarded as the more reasonable position. Why people who are atheists should wish to dilute their opinions is unclear, seeing as most theists do not seem to have similar reservations about their own religious beliefs.
I have heard the argument that atheists are as closed minded as theists, that they simply take the polar opposite view in not believing in a deity. That an atheist holds firm to the position that there is no god, as a theist does to the position that there is one.
For a start, atheism does not constitute a 'belief system', in the same sense as theism does. Believing in something is not necessarily the same as a 'belief'. You can believe in many things, none of which constitutes as having a belief. I believe I will enjoy my weekend, I believe I will finish the book I am reading. I believe in these things, but none of them are beliefs. We need to be very careful how we use these words, as they do not necessarily mean the same thing. They are deliberately or accidentally used incorrectly, and this just clouds the discussion.
As I stated earlier, although an atheist may not believe in the existence of a deity, given that there is no proof for one's existence, this does not mean that an atheist discards its existence out of hand. Given sufficient evidence, most atheists would change their minds, for the simple reason that atheism is the scientifically rational position to take.
Agnosticism is compatible with both atheism and theism, they simply do not claim to have a position either way. They may be an atheist and be uncertain, or a theist and be uncertain.
There is also a double standard that often crops up. Theists often claim that being an atheist is dogmatic and closed minded. If disbelieving in the existence of a god is dogmatic, then so surely is believing in one.
It is common for someone to be both agnostic and atheist. An agnostic atheist won't claim to know for certain whether or not something claiming to be a deity exists, but equally they won't actively believe that such an entity exists in the first place.