A fandom tool, which allows fans of books, tv shows, anime and the like to write about their favourite characters.
Fan Fiction (shortened mostly to Fan Fics) is represented on many websites, the most dominant being Fanfiction.net and MediaMiner.org.
In Fan Fiction, the writer can either create a story from where the series/episode/book left off (Cannon); create a new world for the same characters (Alternative Realtiy); or mix characters together from different fandoms (Crossover).
Fan Fictions cover all genre, from romance, horror, comedy, to what is known as Hentai (japanese word, for stories of a sexually mature nature).
The fan fiction world is full of a mixture of unreadable, badly written, good and excellent fiction; much like the music industry and its varrying degrees of music quailty.
Some Fan Fiction authors employ betas, to edit their work for them.
As an author myself, I can assert that fan fiction is a fun way of carrying on a much loved and ended fandom. It is a way to improve one's writing, as most websites have the facility to recieve instant reviews and so allows the author to gain Constructive Criticism. (On the downside, some readers 'Flame' work they disagree or don't like.) It also allows those who are not inclined to write to read about their fandoms and keep the memories of their favourite characters alive.
Fangirl #1: "Omg, my favourite author just updated her Twilight Fan Fiction!"
Fangirl #2: "Kya, this site has lots of Kurama x Kagome crossover fan fiction!"
Fanboy #1: "Ewww, whose idea was it to pair Harry Potter and Professor Snape??? *reads on*..I'm scarred, I'm scarred for life!!!!"