Fan fiction (alternately referred to as fanfiction, fanfic, FF or fic) is a broadly defined term for fiction about characters or settings written by admirers of the original work, rather than by the original creators.  The term usually applies to works that are not commissioned and unauthorized by the copyright holders of the original and usually (but not always) works which are not professionally published. Fan fiction is defined outside of original fiction, which exists within its own discrete, professionally published universe, and therefore -- as long as it's related to the subject -- can be completely outside of canon works within that universe. Most fan fiction writers assume that their readers have knowledge of the canon universe (created by a professional writer) in which their works are based. (Copied from the Wikipedia article on fan fiction.)
History and StarDestroyer.net
StarDestroyer.net has a long history of fan fiction, particularly in the area of Star Trek vs Star Wars. This dates back to alt.startrek.vs.starwars, where as early as 1998 some fans had been publishing their crossover stories on the Usenet group. Most of these stories have been archived for posterity on Rob Dalton's ASVS Fanfic Archive.