Definitions:

Fanfic
Fan fiction - story written about a televison show, book, comic or movie by people un-connected with the original and without any intention of making a profit.

Fanart
Graphic of some kind for a television show, book, comic or movie by people un-connected with the original and without any intention of making a profit.

Slash
A story involving a romantic or sexual relationship between characters of the same gender. Originated from Star Trek Kirk/Spock fandom, and the slash (/) put between the names.

Femslash
Slash fiction that involves two female characters, female/female.

Alternative Fiction - Alt fic
This is another term used for slash fiction, particularly in the Xena fandom.

Fandom
A term for the fans of one particular show or genre.

Canon
The events, characters and relationships that have occurred within the actual television show, book, comic or movie.

Bard
Someone who writes fan fiction - the term comes from the Xena fandom but is sometimes used by writers in other fandoms.

Uber
A type of story that involves new characters who are similar in personality/appearance to canon characters. A rapidly growing type of story, especially among the Xena fanfic writers.

Alternate Universe - A/U
Essentially all fanfic is alternate universe, but it is a term most commonly applied to stories where either the canon characters are placed into a new setting or a facet or multiple facets of canon are altered.
For example if the characters from Bad Girls worked in a hospital instead of being prisoners/guards. Or if Annika Hansen had never been assimilated by the Borg.

Ship
Short for relationship - used to show which characters are together in a particular story.

Shipper
A shipper is someone who believes certain characters belong together to the exclusion of all other possible pairings.

Subtext
Usually refers to images, dialogue and characterisation that implies a sexual attraction or relationship between characters. This is very subjective and will often be met with looks of bewilderment by others, although if you watch Xena you'd have to be blind or in deep denial not to see it - even my mother saw it and most things whizz right past her head.

Maintext
This means the relationships that actually exist on the show etc. For example Willow/Tara or Torres/Paris.

Vignette
Short story dealing with a brief period of time and single subject.

Challenge
Common on fanfic writing lists and websites, someone literally challenges others to write a story with certain ingredients.

Crossover
A story that includes characters from different shows etc. some of which can be related, others not. For example a DS9 and Voyager crossover or a Buffy and Xena crossover.

First Time
Story that explores the characters' first romantic/sexual encounter as a couple.

Erotica
A tastefully written sexual story - the difference between this and a PWP lays in the style of writing and language, but the line can be thin.

PWP
Plot, What Plot? or Porn Without Plot - stories written purely to show the characters engaged in sexual shenanigans.

BDSM
Bondage, domination and sado-masochism.

Mary Sue
An original and overly perfect character created by the writer and often acting as their alter-egos. They often end up bedding other characters or acting as matchmakers for the intended ship.

Turbo-fetish
Tongue in cheek name for the spate of 'stuck in a turbolift' stories that have become part of the Torres/Seven fandom - and I don't know why you're looking at me like that cough.

Spoof
A humorous story that pokes fun at the fandom or even the writers - tongue in cheek and friendly.

Round Robin - RR
Story written in installments by different writers, usually impromptu.

Angst
Putting the characters and by extension the readers through deep emotional and possibly physical pain (characters only for the physical - fanfic rarely maims, unless you count papercuts.)

Hurt/Comfort H/C
Similar to angst, the characters suffer some form of pain or anguish but unlike with pure angst you do get the comfort part as well.

POV
Point of View - the viewpoint from which the story is told.

Spoiler
Information within a story that can reveal plot points for possibly unseen episodes of television shows, books, comics or movies.

Beta Reader
Someone who checks the writer's work before publication to make sure there are no spelling/grammar/plot/characterisation mistakes. Or in other words someone who can stop you from making a right pig's ear of it.

Feedback - fb
Response from readers or watchers either by e-mail, chat or in person. It is the bread and butter of fanfic writing and graphic design, and encourages many writer/designers to keep on creating.

Constructive criticism
A form of feedback where the reader offers suggestions on ways to improve the story - polite and helpful are the keywords here.

Flame
To insult someone's work or them in a vicious manner - knuckle-headed idiot with delusions of grandeur is the keyword here.

Archive
A collection of fanfic available on a web site - you're on one now. Or an automatically logged collection from a mailing list.

Archivist
Someone who owns/runs an archive for fanfic or fanart - which would be me in this case.

OTP
One True Pairing - the sole pairing that a person ships in a particular fandom.