It's hard to explain, especially to a theist. It simply means no belief in deities. Nothing more, nothing less. It does not imply an act of rebellion against whatever god/s the theist I'm speaking to happens to believe in. It does not imply worship of their god/s antagonist-like satan to the xians. It doesn't imply anger or other emotions towards any god/s. Really, it just means we don't believe in your, or anybody else's, deity.
It also doesn't imply that all atheists think exactly the same thing. Lack of belief in a deity of some nature is about all most atheists have in common. Within the atheist community (if you can call it that) you will find pro-life and pro-choice supporters; some who support the death penalty and some who vehemently oppose it, skin color varies wildly, some are Democrat, some Republican, some 3rd party supporters. We live in all countries on this amazing planet, speak different languages, eat different foods. I hope my point is sinking in a little. You can no more lump all atheists together than you can theists.
Atheism is not the same thing as anti-religion. While some atheists may want to see an end to religion, that's not what the word means or what all atheists want. I for one think religion has a purpose for some people. No good can come from forcing people to give up their faith, than forcing faith on those who don't believe. It's a lose/lose scenario.
I'm not going to dispute the fact that there are some militant atheists. But let's face it, there are extremists in any group. Heck, even I find them annoying.*coughRichardDawkinscough*. They aren't any more annoying than a theistic group who tells atheists they should "get out" of a given country or they'll burn in a hell the atheist doesn't believe in. In a conversation like that, both sides end up looking like losers.
Theists have a hard time understanding atheism. It goes against a fundamental way of thinking for them-and I can respect that. I can't understand a belief in something that doesn't exist, I certainly don't expect anyone to try and understand my point of view, just respect it. If you have any questions, please feel free to ask them. I'm not the fastest at responding, but I will get back to ya.