Fan fiction (usually abbreviated to fanfic) is unauthorized creative writing that is derivative of another work, generally by members of that work's fandom as a form of celebration. While that's the literal extant of the term, it's often misused to refer to either a specific subgenre of fan fiction (either slash fic or Mary Sue) or as a dismissal on the basis of lack of originality regardless whether or not it's directly derivative (e.g. calling Eragon "the cheap crossover fanfic of Star Wars and Dragonriders of Pern"). While fan fiction is technically copyright infringement, most rights holders are okay with it so long as it's clearly labeled and no attempt is made to profit off the work.
The fan fiction community is one of the few fandom circles that has a vast female majority (how it ended up that was is unknown). This has often resulted in conflicts between different "sects" of a fandom that often turns to outright dismissal and misogyny. Fanfic writers are often pigeonholed as approaching the original work on a shallow basis, only participating at all on the basis of attraction to the male characters and the desire to pair them up romantically regardless of genre or context.
Even within the fan fiction community, a lot of circles have an undercurrent of misogyny that manifests around female characters.