Atheism is the lack of belief in any god or gods.
Put more clearly, atheism is a philosophical position negating the validity of belief in the existence of any form of non-evolved complex being.
It could also be called a philosophical position opposing belief in any simultaneously omniscient (that is, all-knowing), omnipotent (all-powerful), omni-benevolent (all-good) supernatural being.
The trouble with defining atheism does not lie within the core of its philosophical position or argumentative validity. On the contrary, it is a very strong and diverse philosophical position, with a number of separate but mutually cohesive arguments existing in its defense.
The trouble lies instead in that atheism is non-theism – the point here being that it is a “non.” It says “not-this” quite clearly, but doesn’t, in itself, supply what many mistakenly assume should be coupled with it: a “this instead” statement.
Atheism is the “not-this” without the “this instead,” and thus, being a negative position, it is difficult for some to understand or accept, even when defined perfectly and simply.
Atheism is expected, especially by theologians and religious laypeople, to be an entire self-sustaining theory of how the world works. However, this is not what it is. It is a partial statement of a worldview, not an entire one.
People who are atheists do not believe in god.
This does not mean they do not believe in anything. Critics assume this only because they misinterpret the atheistic position to stand for more than it actually does, ie, to stand for all of what one disbelieves as well as all of what one believes.
Such a misinterpretation is often found in arguments made by theists because, no doubt, this is how religion works. If I say, “I am a Christian,” I simultaneously make a statement of what I both do and don’t believe, because Christianity, just like all other religions, contains in its definition what is both believed and disbelieved by its members.
Atheism is not required to fit this sort of rigorous encapsulation of a worldview. It is for this exact reason that it does not belong grouped in with a list of religions as just-another-option.
An atheist can embrace many different theories and ideas about how the world works.
Any atheist can take and keep what parts of Buddhism, Daoism, Christianity, evolutionary theory, quantum physics, etcetera, seem philosophically and morally valid, and still remain an atheist. An atheist is free to graze, picking and choosing reasonable worldviews from many different schools of thought.
In a nutshell, atheism embraces free thinking, reasoning, judging, and valuing. That, in particular, is one of its greatest assets. I am an atheist and a philosopher. I am free to embrace the philosophies of Jesus, the Buddha, Darwin, Lao Tzu, and Dawkins simultaneously (if I choose to) without fear of reprisal outside of maintaining a worldview that fits within reason.
Atheism, like agnosticism and anti-theism (also known as militant atheism) is not a religious position, but a philosophical position about religion.