A story written by a fan of a particular ard (movie, book, tv show, video game, etc.), about the characters and world in that series, usually without the original creator's permission.
Fanfics are fictional stories written about pre-existing books/films/animes/mangas/etc by fans of this work. A Disclaimer is included as standard, stating in some way or another that they do not own the characters they are writing about.
Some authors (e.g. J.K. Rowling) have encouraged fanfics on the grounds that publishing is not attempted (this will always result in a law suit, something the authors of fanfics have generally accepted). However, other authors (e.g. Anne Rice) have requested that fanfics based around their stories(etc) are not posted on fanfiction sites. These such authors are more commonly known as Kill Joys (see bitching).
Many people love fanfiction. Others hate the thought of it.
Fanfic hating dude: Please go die in a fire.