A troll is someone who makes irrelevant or purposefully offensive posts in order to invoke emotional responses. A troll is not looking out for the forum's best interest or trying to generate good conversation, just seeing who he/she can anger. The act of disrupting the forum in this way is referred to as trolling. Trolls are generally recognizable and uninteresting, although some are able to come off as sincere.
Since trolls are trying to generate lots of angry replies to posts, actually supplying those angry replies is what makes them stick around to keep trolling. Replying to a troll, especially in an emotional-sounding state, is known as feeding the troll.
Sometimes it can be hard to tell whether or not a user is a troll or just ignorant. Generally, it is best to bring it to a moderator's attention and they will discuss whether or not to ban, warn etc. Mods are usually good about getting rid of the evidence of a troll. Usually telling the troll upfront that they're trolling isn't productive. Keep in mind that with the new forum, you can add someone to your Foe list and not have to see their posts.
The golden rule is: DNFTT (Do Not Feed the Trolls)
If you have been accused of being a troll, either ask specifically why others feel this way or take a step back and read the FAQ ten times. You could be trolling and not even fully realize it. Flame-wars only solidify your position as a troll.
See also: Rules for online debate