DPS or Damage Per Second is generally considered a MMO term, which describes how much a character, spell, skill, ability or item can produce on average per second, with high and low evened out.
The term is used in Diablo 3 by the design team, when they stress the fact that (as was the case in Diablo II) all characters are capable of fighting and succeeding alone or in a party. In other words, there are no healers or tanks or mages who can only do one thing, and aren't capable of surviving or thriving on their own.