In World of Warcraft, player vs. player (commonly abbreviated PvP) denotes player versus player combat of any kind such as:
Dueling - one vs one combat in a controlled environment.
Battlegrounds - group vs group combat in a competitive environment. Players that complete a battleground receive 'marks' for the appropriate battleground, which are used as a sort of currency to purchase rewards from PvP vendors.
Random PvP - whenever a player comes across another player of an opposing faction whose PvP Flag is turned on (or if two players meet in a contested territory) that player can engage the other one in combat. This is different from the other types because this is an uncontrolled environment. Players do not have the ability to choose their opponents. In Battlegrounds you will be fighting people close to your level. In dueling you can choose who you wish to fight. In Open Combat (only seen on PvP servers, in the Arena, and any time your PvP flag is on) players 40 levels higher than you can choose to fight you if they so desire and you cannot decline. 10 players of an opposing faction can gang up on you when you are soloing and you cannot decline. However, if you happen to spot some members of the other faction of a reasonable level, and you're ready for a fight...