A couple of thoughts. As an Evangelical, I define an atheists as a person who has proof that God does not exist. Is this accurate and if yes, what proof was the clincher for you?
Lets give thomas15 some credit, people. He asked an honest question and asked me to confirm his belief. He was not dogmatically asserting his own definition of Atheism, but merely put what he thought out there and asked for confirmation. So I'd appreciate it if everyone refrained from mocking him for saying something he didn't say. Now for my answer.
Your definition is incorrect, at least in my case. The word "atheism" can be broken down into two parts: "A" meaning "without" and "Theist" meaning "Someone who believes in a God" (some attach the belief in personal revelation to the word theism, meaning that theism is belief in the "whole package" of a God that communicates his will to select human beings. In contrast, a deist is a person who believes in God but not in personal revelation, which is the root of religion. Notable Deists include Ben Franklin and Thomas Jefferson). So technically, an Atheist is someone who does not believe in a God. Now, there are those who may believe firmly that God does not exist (I am unaware of any atheists who do, however. Even Richard Dawkins does not go quite this far), and those are typically defined as "Strong Atheists." Richard Dawkins, a popular Atheist figure, actually has a sliding scale of seven levels of atheism, with 1 being purely agnostic to 7 being absolutely sure no Gods exist. He describes himself as being between 6 and 7, very close to 7. Personally, I am not as high on the scale. My beliefs are dependent upon the evidence and so far I have not seen compelling enough evidence to change my viewpoint.
Let me explain what it means when most atheists say "there is no God." Have you ever heard the phrase "there is no such thing as ghosts"? Perhaps you've even uttered it once or twice in your lifetime. Now, you might believe in ghosts, but there is a sizeable population who don't. Why? Not because they have proof that ghosts don't exist, but because they haven't seen good evidence of them, and therefore simply do not believe. So why would someone say "there is no such thing?" To understand that, one has to understand the difference between absolute certainty and practical certainty.
Absolute certainty is the active belief that something is absolutely true or absolutely false, with no gray area in the middle. No atheist I've ever heard of is really and truly absolutely certain that god doesn't exist. It is impossible to be certain of anything that is unfalsifiable (something that is falsifiable has realistic criteria that can be met before it is considered false. God or anything supernatural is unfalsifiable, meaning that there is no realistic criteria in order to prove it false), but one can gauge the likelihood of an unfalsifiable claim to be true.
If I told you there is an invisible horse named Ricky sitting next to me right now, you'd have no way to prove that false. So would you need proof that Ricky doesn't exist in order to say that you don't believe me? I'm going to guess no. You wouldn't believe me because invisible horses are a ridiculous and unlikely idea, but even then you could not be absolutely certain, because given enough caveats there is no situation in order to prove me wrong. Doesn't sound fair does it? That's where practical certainty comes in. If you tell me "I don't believe you, invisible horses aren't real," then you would be saying that with practical certainty. Practical certainty is the belief that something is true or false based on the likelihood of it being true or false. I am practically certain we are not all living in a dream world a la the Matrix, but I can't prove we aren't. If new evidence were to come to light that demonstrates it as fact, then I would reevalutate the likelihood and change my belief. The same goes for God. I don't think a God is very likely, therefore I am practically (not absolutely) certain it doesn't exist. But if very compelling evidence were to appear on the subject, then I would reevaluate my position. That's the key difference between practical and absolute certainty. When someone is absolutely certain about something, he or she will not change their mind regardless of any new information. When someone is practically certain, he or she will at least consider changing their mind in light of new information on the subject.
Finally, I want to leave you with some thoughts about burden of proof. Although I covered this in my previous comments, I feel it bears repeating. If you think back to my invisible horse example, what would cause you to believe my story? My presenting evidence to support my claim would probably be more compelling than a few "eyewitness" testimonies, am I right? Well this all ties into the burden of proof. If I am the one claiming that there is something out there that nobody else can confirm and verify, then the burden of proof is on me to prove my claim. Those who believe in God are the ones making the claim, and therefore the burden of proof is upon them to support their position. My position is simply "I don't believe you, prove it."