A toon is a synonym for a character in a video game that is a role-playing game, usually used only in the context of Massively Multiplayer Online Role-playing Games (MMORPG), such as World of Warcraft.
Character, avatar, or toon are synonyms in this context.
(Avatar is a misnomer, however.)
In role-playing games, a great deal of effort is spent in creating a unique persona or character before play begins. During character generation, the player makes choices that will affect the gameplay, such as appearance, name, gender, race, and class. Once created, these characteristics are immutable, as they define the play experience. The selection of class determines the strategies the character will use to succeed.
In short, Role-playing games have great replay value because a player can re-experience the game using a new character or toon.
Toon is presumably a contracted form of cartoon; video game characters are animated, after all. The origin of this term can be attributed to the standard root of all leetspeak (internet jargon): a need for efficiency for lazy typists.
Toon is probably used because it is shorter and easier to type than the word character. Anyone familiar with these games can easily surmise the meaning of the term from context. Furthermore, the term avatar is avoided as it can possibly create confusion. In roleplaying games, avatar also refers to the incarnation of a deity.
I have 6 toons, so I have all the professions spread among them and I can craft anything!