The default atheist position, which is held by the great majority of the atheist community, is that atheism is a "lack of belief". Obviously, this means that atheists do not have a belief in any gods. However, this does not imply that atheists believe no gods exist.
For many, this can sound very confusing. If someone told you that they read Santa Claus was coming to town, there are a few relevant positions to take:
Both the first and third positions express explicit beliefs. However, the second position did not accept the person's belief that Santa was coming to town, thus lacks a positive belief about Santa coming to town. While the second position lacks a positive belief about Santa's arrival, it also lacks the opposite belief that Santa is not coming to town. A common response from someone taking the second position might be, "Don't believe everything you read! Maybe he's coming, but I haven't seen anything that would make me believe so." This is quite different from an example response from someone taking the third position, "I don't care what you read! Santa has never come to town before, and I certainly do not believe Santa is coming to town now."
This distinction is amplified by claims of knowledge. The equivalent claims to knowledge of the positions above make the issue a bit more clear:
Now, both the first and third positions are making claims to knowledge. Atheists generally consider either of these claims, with respect to the existence of gods, intellectually dishonest. Unfortunately, this distinction is often lost during discussions between theists and atheists because most of the conversations consist of colloquial (informal) language as opposed to a technical, philosophical discussion which recognizes the epistemological differences between knowledge and belief.
This often leads theists, which frequently are making a positive claim to knowledge about the existence of gods, to ask a question in which an atheist replies coloquially, "There are no gods." Understandably, from the perspective of the theist, the atheist has just made a claim to knowledge which can then be followed by a theist's request for proof. However, because the atheist's true meaning was in the context of belief and not knowledge, a misunderstanding is created. When the atheist states that the burden of proof is on the theist and the atheist doesn't have anything to prove, the conversation declines. Because of the atheist's miscommunication, the theist now feels justified in their belief that the atheist is simply making claims to knowledge on faith, just like he/she is. On the other hand, the atheist gets increasingly frustrated that the theist does not understand where the burden of proof lies and feels justified in their belief that the theist is simply avoiding the question because they have no proof.
If some of this sounds like agnosticism to you, that is because it is. Agnosticism deals specifically with the realm of knowledge, whereas atheism is in the realm of belief. In this context, gnostic (not to be confused with the Gnosticism associated with early Christianity) simply means "with knowledge", while agnostic means "without knowledge". This lack of knowledge can either refer to the absence of the knowledge which is available, or to the notion that it is not possible to possess the knowledge. Since a label of gnostic or agnostic usually tells nothing about what a person believes, only if they have an unspecified knowledge, it is of limited use. Instead, labels related to belief (theism and atheism) are more common. Though the two types of labels are most descriptive when paired, the knowledge-based label is often absent. This is often either due to a poor understanding of the differences between the four labels, or because the belief-based label implies it as its default state.
Since generally atheists believe people are born without knowledge of the concept of gods, thus do not have an innate belief in any gods, the default atheist position is an agnostic-atheist. If an atheist then encounters a god belief and does not accept it, the person remains an agnostic-atheist. However, if the person encounters the god belief and then claims to have knowledge that the god truly does not exist, the person is a gnostic-atheist. Most gnostic-atheists are those that have either not seriously considered their position, have a poor understanding of the topic, are being intellectually dishonest, or are really agnostic-atheists. The last type understand the nuances of the issue but claim their knowledge is sufficient to warrant the gnostic label if they wish to use it, unless pressed with a strict definition of knowledge. This last group is often the cause of much of the confusion, since they commonly use the colloquial understanding of knowledge when making statements about the existence of gods. Unfortunately, the gnostic-atheist label is rarely used by gnostic-atheists due to an ironic lack of knowledge. Instead, these people ambiguously use the atheist label, which implies the default agnostic-atheism. This creates additional confusion as to what atheism is. Additionally, more confusion is introduced when the agnostic term is often mistakenly used instead of [agnostic-]atheist since the person intends to mean while they do not have the knowledge of the true answer, they do not hold a positive god belief either.
While the line is relatively clear-cut in terms of the default atheist position, the theistic view of the default theist position varies greatly. Even within the Abrahamic religions, there is a great deal of diversity of thought regarding innate knowledge and belief. A very common theistic view that is also most apt for confusion during discussions with atheists is that a person is born with the belief/knowledge/both of their god(s), with this claim to knowledge instead being supported by the concept of faith. Not only does this understanding of knowledge differ from the atheist, but it places the default theistic position to be gnostic-theism, the opposite of the default atheist position. The result is the theist not only using a different understanding of what constitutes knowledge than the atheist, but also assuming the atheist is coming from the gnostic perspective. Due to this misunderstanding, many conversations do not get past this point.
Four common statements can illustrate each of these perspectives:
You are now equipped with a good understanding of what an atheist is (and is not). During discussions, be sure that everyone is on the same page in terms of which category each person belongs in -- and even which definition of "god" will be used. If your arguments are not even directed at what the person actually believes/doesn't believe, you're wasting your time. [Gnostic-]theists should know that if they want to debate with an [agnostic-]atheist, asking the atheist to prove that gods don't exist does nothing but make the theist look clueless. This also holds for gnostic-atheists asking agnostic-theists to prove gods exist -- though I hope by this point in the reading, the gnostic-atheists would no longer consider themselves gnostic.
Note to theists: People that actually believe that god(s) exist but say they do not follow them because they hate the god(s) are NOT atheists, they are simply theists that are angry with their god(s). This is also one of the definitions of "anti-theism". I find that often some theists actually refuse to believe that an atheist does not accept that a particular god exists. If you are one of these people, please try never to be guilty of this again. If you really want to "reach" the person, attempt to show evidence why the atheist should believe that the god exists instead of acting as though you know more about what the person thinks than what they do.
-LackOfBelief