What exactly does "fap" mean? [NSFW]

For the sake of giving this a fun answer in case you're asking in earnest...

Fap is an internet neologism, an onomatopoeic intransitive verb referring to the act of male masturbation, whose sound is imitative of the associated slapping of testicles against the body. Fapping refers exclusively to male masturbation; female masturbation is (in context and by association, but very rarely in practice) referred to as paffing or squishing. Reportedly it has its origins in the Japanese-language comic sound effects used in manga, in reference to the same act.

'fap' is a slang term. We have many slang terms in English, some more familiar (or crude) than others, for masturbation. They all signify the general, uh, "process," if you will.

Actually, the word fap has existed in English for a long time meaning drunk to the point of befuddlement, as in Shakespeare's "Merry Wives of Windsor":

Bardolph: Why, sir, for my part I say the gentleman had drunk himself out of his five sentences.

Sir Hugh Evans: It is his five senses: fie, what the ignorance is!

Bardolph: And being fap, sir, was, as they say, cashiered; and so conclusions passed the careires.

In it's more recent meaning that refers to masturbation, its usage is somewhat different. It is onomatopœtic of course, and when used it is normally intended to have a comic false obliqueness (it pretends to be subtle, when really it's less subtle than just saying "masturbate"). So one might say "fap, fap, fap" meaning "I am going to think about this later while masturbating", as a crude joke.

It's popularity is generally credited to the web-comic "Sexy Losers", (considerably more NSFW than this page, google if you want to find it), whose author has said:

It was pulled from the Viz translation of Heartbroken Angels. Although there were a number of sounds the translator used for masturbation (there’s a lot of that going on in that comic), I chose the word fap as it came from a particular strip that had god masturbating.

Unlike masturbation, fapping is, exclusively, the auto-erotic stimulation of the penis. Fapping is not used to describe intellectual, mutual, anal, or vaginal masturbation.