Player Kill
Player Killing refers to non-consensual PvP, usually in the form of an ambush by the PK (Player Killer). There will not be any support for PKing in Diablo III, since all PvP is going to require player consent. How exactly this will work has not yet been determined, or at least not related publicly.
Though Diablo II allowed for non-consensual PvP, most modern RPGs do not. Dueling is almost always allowed, but each player must agree to it, either at the time of the duel, when joining the game or entering the PvP-allowed area, or sometimes upon character creation or realm assignation.
It's widely hoped that Diablo III will feature more robust support for PvP, with features such as PvP ladders and arena games. The D3 Team has not yet confirmed any such features.