Slash fan-fiction is particular genre of fan-based writings that stars one or more characters from a movie, tv show, or book in a romantic or sexual (typically the latter) pairing that does not usually occur in the actual plot of the respective media.
Legend purports that the original Slash story was one that featured Kirk and Spock doing the nasty. Jessica Sinclair in her article on beyonddreamspress.com supports the theory and suggests it as being an idea that emigrated from England in the 60s.
Slash remained an underground thing until the advent of the internet, where, like many things of proper culture, it proliferated in the unfiltered web.
The term slash was coined after the "/" symbol, which was used in the story codes to signify what kind of pairings occured: m/m would be a gay male pairing, m/f a straight pairing, etc. The gender letters were often replaced by character names producing such results as "Harry slash Snape" or Harry/Snape (or in even more shortened forms, H/S). Slash, however, has a very strong conotation for being of same-sex or bisexual pairings. Heterosexual slash is often just called erotic fan-fiction.
While Slash tends to proliferate for popular shows or cult favorites, sometimes more obscure shows attract a very strong slash fan-base. Examples include the Invisible Man TV series, Hercules: the Legendary Journey, and the Pretender.
Slash is often debated, as typically the larger fanbase shuns the slash fans. Arguments over whether it is right to use someone else's creations in that manner abound, though the debate usually remains only on a moral basis as few copyright holders try and take fan-fic writers to court and the legality of gets entrenched in the battle between free speech and intellectual property.