PvP: The title is a bit misleading, because it's realy faction-versus-faction, horde-versus-alliance. There are three types of areas: friendly, hostile, and contested. In friendly territory you can attack players of the other faction on sight, but they cannot attack you. In hostile territory it's the opposite. In contested areas, everyone of the opposing faction is free game. You see someone of the other faction and wanna kill him? Go on ahead. Or ignore him, but be careful that he doesn't stab you in the back. Better to kill him.
You can also challenge people of your own faction to non-lethal duels.
Normal: on these servers there is consentual player-versus-player conflict. Normally no other player can attack you. You can change this status ("flag" yourself) through one of the following options:
1) Attacking a faction NPC
2) Attacking a player "flagged" for PvP, or
3) Typing /pvp
I'll give you an example. I hang out on Test 1, a normal server. However, last night a massive group of Night Elves came down from Ashenvale on a raid. They had flagged themselves for PvP by attacking the guards in the North. A large number of Horde players assembled in Crossroads to fight them off. They readied themselves by typing /pvp so that they could jump in and kill on sight. Myself, I was busy questing at the time and my lag was bad, so I wanted none of that. I could have walked directly through the Night Elf raid and they couldn't have touched me.
Oh yeah, the story. Although the Horde defenders fought well, it was really the level 40 Crossroads guards that destroyed the Night Elves. Moral: even when you have a lot of people, it helps to be withing 20 levels of your enemies.