A player killer (PK) is a player who attacks other players, rather than just/only the monsters. PKs might also be duelers interested in PVP, but the term is more often used to describe players who force non-consensual combat; sneak attacks and ambushes and other behaviors that can be considered griefing. Diablo II allows PKing, though there are various limits placed on when, where, and how players can go "hostile" to each other, as well as damage penalties and other controls to level the playing field. Read more about those here.
PKing or Not?
There is always heated debate about how much, if at all, RPGs should support PKing. Almost no one argues against dueling, but whether the PvP combat should ever be non consensual is the big question. Most early RPGs allowed it, most modern ones do not. Players must select PvP upon character creation, or by the realm they play on, or by the game type they join, but in almost all cases it's possible to avoid PvP entirely, if a player so desires. World of Warcraft does not, and Diablo III will not, allow non-consensual PvP.