Realm versus realm, often abbreviated as RvR, is a type of gameplay where players band together as a faction in order to battle against an opposing faction. The strict interpretation of realm versus realm comes from MMO "Dark Age of Camelot", where three "realms", or factions, vye for control of the land.
In later video games, such as World of Warcraft and RIFT, realm versus realm is implemented in the form of battlegrounds, which are self-contained arenas where a group of players from opposing factions do battle, without interfering in the wider world.
EVE Online also has a similar approach to RvR, called factional warfare, where players battle over territory by "enlisting" in an NPC corporation explicitely designed for players to co-ordinate strikes against targets allied to opposing empire factions.