since an atheist doesnt necessarily know that he/she is an atheist, or what atheist means, why would we ask this atheist to define a concept he/she doesnt know and isnt aware of not believing in?
In its most common usage, "atheists" are usually taken to be narrowly construed as people who know what gods are and reject belief in such beings. Every culture and theistic religious tradition has a specific set of gods (or a single god) with specific characteristics. Atheists naturally tend to be focused on rejection of belief in the gods that they are most familiar with, but they tend to reject the entire class of beings as implausible. Not worth believing in any more than other mythical beings that they are familiar with from folk tales or cultural narratives. For the sake of reference, I'll call this conventional type of atheist a "narrow band atheist". In this sense of "atheist", a baby would not be considered an atheist, because babies have no concept of deities to reject belief in.
On the internet, where debates over the existence of gods tend to be popular, there is a very broad sense of "atheist" that is popular, especially (albeit not exclusively) among atheists--that anyone who simply lacks belief in gods should be considered an "atheist". People get very defensive of that usage, perhaps because it turns the category into a sort of natural "default" word sense that is very easy to defend in these kinds of polemics. That's ok. Words can have a range of meanings. I'll call this usage for "atheist"--probably the usage most preferred by the TFT community--as "broad band atheist". In this sense of "atheist", babies might be considered atheists, because, not knowing what deities are, they simply lack a belief in deities.
So, to answer your question, we would ask narrow band atheists what it is that they reject. They would answer by describing the properties of beings that are conventionally referred to with common nouns like "god" and "deity". These words are defined in every English dictionary, although I always caution people not to confuse definitions with full-fledged word meanings. Like any meaning that we associate a word or expression with, the meaning of "god" is a tangled, structured web of associations. Definitions are just concise heuristic pointers to a word meaning in common usage.
A narrow band atheist would defend rejection of belief by explaining why such beings are implausible. That's not terribly difficult, but it is still easier just to demand that theists try to defend their acceptance of belief in the particular god or gods they profess belief in. Juma, I think that you are trying to work with the broad band concept of "atheist", so it makes sense to ask what possible definition of unbelief they could have. That is because your preferred usage includes people who consciously reject belief in gods and those who simply don't know what gods are or don't care to think about them. In that context, it doesn't always make sense to demand that atheists define what they don't believe in, because they could simply lack a god concept.