Answer:
The difference between atheism and agnosticism is the difference between belief and knowledge: atheists cannot say that they believe that any gods exist and agnostics cannot say that they know for sure (or perhaps that anyone can know for sure) if any gods exist or not. Agnosticism and atheism are not mutually exclusive; instead they are orthogonal because they are about separate issues
"A" means "without" and "gnosis" means "knowledge." Hence, agnostic: without knowledge, but specifically without knowledge of gods. Knowledge is a related but separate issue from belief, the domain of theism and atheism. This means that, contrary to some popular assumptions, agnosticism is not an "alternative" to atheism and theism.
Agnostics may or may not also be atheists; technically agnosticism shouldn't necessarily incline a person one way or another but as a practical matter agnosticism today seems to be more likely to occur alongside atheism rather than theism.
Gordon Stein wrote in his essay "The Meaning of Atheism and Agnosticism":
Obviously, if theism is a belief in a God and atheism is a lack of a belief in a God, no third position or middle ground is possible. A person can either believe or not believe in a God. Therefore, our previous definition of atheism has made an impossibility out of the common usage of agnosticism to mean "neither affirming nor denying a belief in God."
Actually, this is no great loss, because the dictionary definition of agnostic is still again different from Huxley's definition. The literal meaning of agnostic is one who holds that some aspect of reality is unknowable. Therefore, an agnostic is not simply someone who suspends judgment on an issue, but rather one who suspends judgment because he feels that the subject is unknowable and therefore no judgment can be made.
It is possible, therefore, for someone not to believe in a God (as Huxley did not) and yet still suspend judgment (ie, be an agnostic) about whether it is possible to obtain knowledge of a God. Such a person would be an atheistic agnostic. It is also possible to believe in the existence of a force behind the universe, but to hold (as did Herbert Spencer) that any knowledge of that force was unobtainable. Such a person would be a theistic agnostic.
If I ask "do you believe that any gods of any sort exist," then "I'm agnostic" does not answer the question because "agnosticism" refers to your state to knowledge, not beliefs. Either some sort of belief that some sort of god is present or not; if it is then you're a theist and if not then you're an atheist. There is no "third way" between the presence and absence of a belief. You may not know for sure if you should believe or not and it could be that you waver between believing and not believing, but those aren't "third ways."