Respec is slang for respecialisation and refers to games where you have a skill, 'talent', 'stat', 'feat' or similar system that you develop as you level up. Respeccing is in that case a matter of resetting all the skill points, feats or the like, and start from scratch, without having to reroll your character.
The word is mostly used in RPG-type games, such as Diablo 3 or World of WarCraft.
Diablo III Respecs
In Diablo II, a character always had all their skills and stats as they were allocated. If you made any mistake, the only solution was to start over. There has not been a definite word on talent/skill respecs, but Jay Wilson has said that he didn't like that you were limited in the old system, and that regardless of how the skill system will look, respecs are probably going to be available.