First, definition: Fanfiction is when someone takes either the story or characters (or both) of a certain piece of work, whether it be a novel, tv show, movie, etc, and create their own story based on it. Sometimes people will take characters from one movie and put them in another, which is called a cross-over.
Most people who bash fanfiction are not willing to look past the fact that it's based on something else to see that it could be worth reading IF you like the subject. If they don't like the subject, then obviously they are going to automatically dismiss the fanfiction.
It is true, however, that some fanfictions are rather poorly written and only a few hundred words, and it is also true that some people just write them so they can have their favorite characters have sex (lemon). But, if you take the time to find something decent, you can end up with a fanfiction story that is so close to the original piece of art, that you'd barely notice the difference.
Sue was so angry that her two favorite characters never got together that she wrote her own story in which the first thing they did was have sex and get married. (Bad example, but sadly sometimes true)
A piece of fiction within a fandom utilizing characters and situations from a pre-existing work including (but not limited to) books, television programs, films, and comic strips.
Typically separated into het, slash, and general genres. Often used to play out AU scenarios and/or various romantic pairings not found in the original work.
Distributed via mailing lists, blogs, and zines. Heavily archived online.
Some of the best stuff I've ever read can be found in the fandom!
2. Amateur fiction of any kind published in fanzines.
She had a piece of fan fiction published in THE CRUDZINE QUARTERLY.
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 #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!!!!"