Player vs Player
In PvP you fight against other people playing the game.
Realm vs Realm
In RvR you are pitted against your foes in a battle to either attack or defend battlefield objectives, keeps and fortresses. Whoever wins can gain control of the area, and ultimately tip the overall war in favor of their side.
Scenarios
Scenarios are timed instances between Order and Destruction players of similar levels. The team that has 500 points or the most points when time runs out, whichever comes first, wins.