A term largely used in MMORPGs (Massively Multiplayer Online Role Playing Games) where you are given the chance to rebuild your character's ability set. This is often granted for free as a result of game changes over time that may have rendered your character weaker.
Some MMO's have implemented methods where you acquire an item to get a respec or you can pay with in game money for one.
This term originated in Dark Age of Camelot, where you distribute points into Specializations when you level.
As a Verb:
"I respec'd into Augmentation so I could be a buff bot."
As a Noun:
"Mythic gave Warlocks free respecs after they were nerfed."