Yup. Player versus player combat. Instead of attacking computer-controlled opponents you're attacking player-controlled. Human intelligence is a huge part of what makes PVP fun because it's never predictable. You could be fighting against two players of the same class and one is REALLY good and the other is REALLY awful. Then of course you need to know your class very well to survive as best you can so there's a high degree of strategy and thinking.
Do you attack the group over here or wait for reinforcements to arrive?
Do you rush in to try an capture the flag solo or do you scout the area for your side?
Do you search the area for cloaked players before doing anything or do you feel confident to proceed forward?
etc... etc...
All those questions come to your mind quickly and you have to make split-second decisions to stay alive while trying to win one for your side.
PVP is broken down into three main categories...
Chaotic Good
This is where everyone agrees to PVP and is done on a large epic scale such as a battleground or an arena
Chaotic Neutral
Players will occasionally attack another player, usually 10 or more levels lower, for no other reason than because it makes the attacker feel better. However the Attacker does this once, maybe twice, then goes about their business. This happens frequently on PVP servers. Chaotic Neutral also occurs when you attack the other sides cities and try and KILL every player and NPC in it. Raiding a city is a fun exercise in survival-skills because not only are you being attacked by players but also by the city guards; more than a few are "elites".
Chaotic Bad
This is when a player will attack the same player over and over and over again to the point where the one being attacked has to call for help. On a PVP server there are roaming bands of players who come to the aid of lower-leveled players when their corpse is being camped.
My brand of PVP is Chaotic Good and very occasionally Chaotic Neutral. Here's a video of my level 73 Death Knight attacking Valiance Keep in Wrath of the Lich King beta. I would definitely call this Chaotic Neutral
http://www.veoh.com/videos/v15602270bgRM5DcY?rank=4&
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Revelation 21:4 "And [God] will wipe out every tear from their eyes,
and death will be no more, neither will mourning nor outcry nor pain be anymore.
The former things have passed away."