Atheism and Agnosticism are all sorts of fun to define. At a minimum you've got 2 varieties of each, more depending on who you talk to.
The main difference is this: Atheism says: "I do not believe in God(s)", Agnosticism says "I do not know if God(s) exist."
Each can be split into "Weak" and "Strong" versions.
"Weak" atheism (which is what most atheists, myself included*, are) says "I do not believe in God(s, but God(s) *may* exist."
"Strong" atheism says "God(s) cannot exist" or "God(s) do not exist"
"Weak" agnosticism says "I do not know if God(s) exist, but may one day find out."
"Strong" agnosticism says "It is impossible to ever know if God(s) exist."
Then you get implicit v. explicit. Essentially, atheism can be further split by if one's atheism is implicit (You don't believe in God(s) because you've never even heard of the concept) or explicit (You don't believe in God(s) despite having heard of the concept.)
Then you get all sorts of other fun divisions.
*I'm somewhere between weak and strong atheism. I do not believe in any deities, and I consider it incredibly unlikely that any exist. However, since it is not completely impossible for them to do so, I could be convinced of their reality if sufficient proof was provided.
Of course, I'm also a bit of a strong agnostic (we split these divisions so fine, and then blend them back together again...) in that I cannot conceive of any proof sufficient to make me believe in an omnipotent deity. However, I also hold that an omnipotent deity would, by virtue of being omnipotent, be able to convince me of their existence if they wished to do so.
In practice, then, I treat deities much like I treat Martians. It's possible they exist, but I'm not going to act as if they do, and if you start making laws based on what Martians want, I'm going to get angry.
