Atheism
Basic description
Atheism is defined as the BELIEF that God(s) does not exist. This is the case not only because Steve McRae says so, but also because Callzter agrees with him... and Callzter is a pretty hardcore Atheist AND the creator of this website (but please don't take this as gospel).
Sematics
Just like with any word that fuels so much controversy, a heated discussion between two or more people, who who use the word "atheism" or "atheist" differently, can quickly devolve into a meaningless and endless discussion on "what-words-mean". In order to conserve a meaningful discussion, it should be agreed upon that the label of a position is rather unimportant compared to the position itself, because labeling a position by a different word wouldn't change the position.
Different usages
Wikipedia gives three definitions of the word "atheism", beginning with the broadest definition and ending with the narrowest. These series of mose inclusive to least inclusive definitions is analogous to the different definitions used for the word "plants" in modern classification.
Atheism - sensu lato (in a broad sense)
"The absence of belief in the existence of deities". Synonymous to "non-theism".
By this usage, an "atheist" is "a person who doesn't believe in the existence of deities". This usage is common amongst atheists themselves. Looking up any website run by self-identified atheists, this definition (often paraphrased) comes up most frequently, but that is not to say that there are no atheists who don't agree with this usage. People who don't agree with this usage often give it the pejorative label called "lack-theism" and would rather use the term "non-theism".
Atheism - sensu stricto (in a narrow sense)
"The rejection of belief in the existence of deities."
The difference between this definition and the former is that it includes stricter criteria for being an atheist. By the former definition, babies would be atheists since they don't believe that a deity exists, but babies are excluded by this definition since they haven't rejected the belief either. In order to be an atheist in this sense, you have be consciously aware of the proposition for the existence of deities and reject that proposition as being unjustified, though not nessesaraly thinking the proposition is false (clarified later on). This definition would also exclude people who aren't consciously aware of the concept of deities, though these are quite rare.
Sometimes this usage is given the label "explicit atheism" to clarify that it is a subset of the former definition, meaning "explicit atheists" are "atheists (in the broad sense)" who also reject the belief in the existence of deities. The atheists who don't reject the belief are sometimes labeled as "implicit atheists".
It can be argued that this definition is more useful than the former one, because when people talk about someone who is an "atheist", most often they don't refer to a baby, nor someone who has never heard about a god before.
Atheism - sensu strictissimo (in the narrowest sense)
"The position that there are no deities."
This usage adds another criteria for being an "atheist" on the former one. According to this definition, an "atheist" does not only reject the proposition that a deity exists, but also believes that the proposition is false, i.e. the atheist believes that no deity exists.
This usage is often not used by self-identified atheists who rather use one of the former definitions. Sometimes this position is labeled as "strong/positive/hard atheism" to clarify the difference between believing that no gods exists and just not believing that any god exists. This definition is favored among theists, especially when in a discussion on the existence of god, theists assert that the atheists has the burden of proof to prove that their particular god doesn't exists (while omitting that by the same logic, they also have to prove that every other god they don't believe in doesn't exists). This definition is also favored among agnostics who (are atheists according to the former definitions but don't use these because they) don't want to be associated with the "proposition that no gods exists" nor with atheists in general, and who can really blame them for that ?.
Why people get so upset about this
Deciding on favoring one particular definition over the other is a double-edged sword. If you use the narrow definition while confronting atheists (who don't identify themselves with that usage), it can really piss them off - especially when you say to them "Oh, you are not an atheist, you're an agnostic." - because it creates a straw-man against them. Self-identified atheists don't necessarily believe that no gods exists and it is better to just let them use the label however they want to use (instead of arguing over the definition and arguing by what label they should identify with) to keep the conversation productive, yet many still do want to argue semantics.
Conversely, if you use a broader definition, you are essentially saying that all agnostics are atheists (since they don't believe in the existence of any god). This can piss off the self-identified agnostics for reasons previously mentioned, and because the label has such negative social stigmas attached to it. Atheists who keep asserting that self-identified agnostics such as Neil deGrasse Tyson are atheists (by their preferred definition of what an atheist is) don't do themselves any favor by acting like pricks who want to pull others into their club. It does only validate the stereotype that atheists are mere assholes on the internet.
The moral of the story, let people identify by whatever label they want, however they want. As long as we are clear on how we use our terms, we can still have productive conversations, even if we don't agree on the usage of these terms.