Respec is slang for respecialisation and refers to a game feature that allows players to partially or completely reallocate the points they have spent in various skills, 'talents', 'attributes', 'feats' or other character values. Respeccing in Diablo 3 will allow players to reallocate most or all of their skill points, thus allowing high level characters to change their play style.
This was not a feature offered in Diablo 1 or 2, where characters could never change their stat or skill points once they were placed. (Respecs were added to Diablo 2 in the v1.13 patch.)
Respecs are a player-friendly feature found in most RPGs, notably Blizzards MMORPG, World of WarCraft.
Diablo III Respecs
In Diablo II, prior to v1.13, characters could not alter any of their attribute or skill points after they were initially placed. Not even a single point, just to fix a mis-click.
The Diablo 3 designers have committed to including some form of respecs in the game, though the precise mechanism remains to be determined. Game Director Jay Wilson has said [1] that respecs will be one of the main gold sinks in Diablo 3, but no other details are yet finalized.