"What is atheism?"
Atheism is characterized by an absence of belief in the existence of gods. This absence of belief generally comes about either through deliberate choice, or from an inherent inability to believe religious teachings which seem literally incredible. It is not a lack of belief born out of simple ignorance of religious teachings.
Some atheists go beyond a mere absence of belief in gods: they actively believe that particular gods, or all gods, do not exist. Just lacking belief in Gods is often referred to as the "weak atheist" position; whereas believing that gods do not (or cannot) exist is known as "strong atheism."
Regarding people who have never been exposed to the concept of 'god': Whether they are
'atheists' or not is a matter of debate. Since you're unlikely to meet anyone who has never encountered religion, it's not a very important debate...
It is important, however, to note the difference between the strong and weak atheist positions. "Weak atheism" is simple skepticism; disbelief in the existence of God. "Strong atheism" is an explicitly held belief that God does not exist. Please do not fall into the trap of assuming that all atheists are "strong atheists." There is a qualitative difference in the "strong" and "weak" positions; it's not just a matter of degree.
Some atheists believe in the nonexistence of all Gods; others limit their atheism to specific Gods, such as the Christian God, rather than making flat-out denials.
"But isn't disbelieving in God the same thing as believing he doesn't exist?"
Definitely not. Disbelief in a proposition means that one does not believe it to be true. Not believing that something is true is not equivalent to believing that it is false; one may simply have no idea whether it is true or not.
"But isn't it impossible to prove the nonexistence of something?"
There are many counterexamples to such a statement. For example, it is quite simple to prove that there does not exist a prime number larger than all other prime numbers. Of course, this deals with well-defined objects obeying well-defined rules. Whether Gods or universes are similarly well-defined is a matter for debate.
However, assuming for the moment that the existence of a God is not provably impossible, there are still subtle reasons for assuming the nonexistence of God. If we assume that something does not exist, it is always possible to show that this assumption is invalid by finding a single counterexample.
If on the other hand we assume that something does exist, and if the thing in question is not provably impossible, showing that the assumption is invalid may require an exhaustive search of all possible places where such a thing might be found, to show that it isn't there. Such an exhaustive search is often impractical or impossible. There is no such problem with largest primes, because we can prove that they don't exist.
Therefore it is generally accepted that we must assume things do not exist unless we have evidence that they do. Even theists follow this rule most of the time; they don't believe in unicorns, even though they can't conclusively prove that no unicorns exist anywhere.
To assume that God exists is to make an assumption which probably cannot be tested. We cannot make an exhaustive search of everywhere God might be to prove that he doesn't exist anywhere. So the skeptical atheist assumes by default that God does not exist, since that is an assumption we can test.
Those who profess strong atheism usually do not claim that no sort of God exists; instead, they generally restrict their claims so as to cover varieties of God described by followers of various religions. So whilst it may be impossible to prove conclusively that no God exists, it may be possible to prove that (say) a God as described by a particular religious book does not exist. It may even be possible to prove that no God described by any present-day religion exists.
In practice, believing that no God described by any religion exists is very close to believing that no God exists. However, it is sufficiently different that counterarguments based on the impossibility of disproving every kind of God are not really applicable.
"But what if God is essentially nondetectable?"
If God interacts with our universe in any way, the effects of his interaction must have some physical manifestation. Hence his interaction with our universe must be in principle detectable.
If God is essentially nondetectable, it must therefore be the case that he does not interact with our universe in any way. Many atheists would argue that if God does not interact with our universe at all, it is of no importance whether he exists or not. A thing which cannot even be detected in principle does not logically exist.
Of course, it could be that God is detectable in principle, and that we merely cannot detect him in practice. However, if the Bible is to be believed, God was easily detectable by the Israelites. Surely he should still be detectable today? Why has the situation changed?
Note that I am not demanding that God interact in a scientifically verifiable, physical way. I might potentially receive some revelation, some direct experience of God. An experience like that would be incommunicable, and not subject to scientific verification--but it would nevertheless be as compelling as any evidence can be.
But whether by direct revelation or by observation, it must surely be possible to perceive some effect caused by God's presence; otherwise, how can I distinguish him from all the other things that don't exist?
"God is unique. He is the supreme being, the creator of the universe. He must by definition exist."
Things do not exist merely because they have been defined to do so. We know a lot about the definition of Santa Claus--what he looks like, what he does, where he lives, what his reindeer are called, and so on. But that still doesn't mean that Santa exists.
That's only a few questions from this:
http://www.infidels.org/library/modern/mathew/intro.html
It's a good read if anyone's interested