DPS or Damage Per Second is generally considered an MMO term, which describes how much damage a character, spell, skill, ability or item can produce on average per second.
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 casters who can only do one thing, and aren't capable of surviving or thriving on their own.
DPS is now also shown on the individual weapons in Diablo III, which some players like and others dislike.