The derivation of the word reveals exactly what it mean to atheists themselves, and atheists should best know what the word means. Thus, atheists are people who are without a belief in a god or gods. Contrary to common belief and some older dictionaries, the vast majority of atheists do NOT absolutely deny the extremely small possibility of God. In order to deny God categorically, an atheist would have to know all possible definitions of God, examine them all, and find them all logically self-contradictory or false, and therefore reject them all. To do this would require the atheist to be omniscient.
Atheists leave that logical mistake to theists.
Since atheists can not logically deny god, they do not. Anyone who says they make such a simplistically all-encompassing statement is simply unfamiliar with the literature of atheism. First, until recently the only people who spoke publicly about atheism were clergymen. Beyond that unfortunate fact, there is the idea that one can deny the existence of a specifically defined god if the definition of that god leads to a logical self-contradiction. OK, so atheists are people without a belief in a god or gods.