It's hard to define atheism.
The simple statement "atheists don't believe in God" is problematic. For a start, it's loaded with the assumption that there is a God for atheists not to believe in.
And so what is atheism? Is atheism the belief that there are no Gods?
Or is atheism just disbelief in all the Gods currently worshipped in our culture?
Or is atheism, as the name implies, simply the rejection of theism as a worthwhile practice?
The short answer is that atheism means different things to different people. Atheism, unlike a religion, is not a single set of ideas shared by a group of people.
Every atheist is different.
So when I say I am an atheist, what do I mean?
Well, it's pretty simple. I believe there are no Gods.
This is a simple statement, but it carries with it a few corollaries:
I believe the Universe came into being through completely natural processes; processes that can be understood if we study them for long enough.
I believe that every religion is just a conflation of the politics, personality and culture from which it grew, and should be understood in those terms.
But most importantly, I believe that we're on our own out here.
There's no supernatural deity calling the shots. The deferral to a God who refuses to show Himself is just a waste of our time.
We're in charge, and it's up to us to make our own way in the Universe.