Atheism is a complex (consisting of many parts) and equivocal antithetical position to the complex and equivocal position of theism. There are psychological, philosophical, political and social components to atheism, and even these components (especially the philosophical) are themselves complex and equivocal. But even given the complexity of the position, it's very very easy to understand.
As a social movement, "atheism" is a broad term of self-identification, legitimately held by anyone who does not believe "God exists" is a true proposition, i.e. anyone who lacks a propositional belief in the existence of any god. Even a "strong" atheist such as myself has to hold this "minimal" belief because of the complex and equivocal nature of theism: Some constructions of "god" (e.g. Yahweh, Allah) are known to be false, some (an omnimax being) are logically contradictory, some (e.g. metaphysical theism, God as the "ground of all being") are meaningless, some (e.g. deism) are unknowable and/or irrelevant, and some are just plain ridiculous. You have to tell me precisely what you mean by "god" before I can tell you precisely why you're wrong. (And if you can't tell me precisely and coherently what you mean by god, that's why you're wrong.)
Even the strong atheist position towards some gods is expressed in specifically knowledge-based terms: I know there's no such being as Yahweh (i.e. the character in the Christian bible is known to be fictional.) Knowledge is never certain; to say I know something is most definitely not to say I'm absolutely certain that something is true. To define knowledge to entail certainty is to define any empirical, scientific knowledge completely out of existence.
Even given the "limitations" of scientific knowledge, the intellectual and epistemic case for the existence of God is closed: We know beyond a reasonable doubt that all the constructions of "god" that go beyond the natural world are wrong, meaningless, irrelevant or stupid. There's simply no point in debating the matter further: Anyone who holds a position on "God" outside of Einstein's (unfortunate) use of "God" as a metaphor for the working of the natural world is either dishonest, incompetent, or deeply ignorant. You can't "debate" such people in any intellectually meaningful sense.
Given that the case is decisively closed beyond a reasonable doubt, atheists in ever-increasing numbers are turning their attention to "cleaning up" the vestiges of this failed paradigm on our society. We want to encourage a rational, scientific view of the world, a world of predictable and knowable natural law, in contrast to the arbitrary and capricious world of theism. We want to erase the social privilege given to superstition: No longer should a belief be immune from criticism precisely because it is ridiculous in some particular way. We want to eradicate a morality that does socially, economically and politically privileges those who claim to speak for God — a privilege that has extended not only to naked imperialism, genocide and slavery but also to enabling and protecting those who rape children — and replace it with humanism, which has as its core the well-being of all humanity.
We know where we want to go, the task is now to get there.