I am a huge fan competition in video games, both direct player vs player and cooperative competition. Competition creates efficiency; it catalyzes and motivates the exploration of a game system. It is through contention that games become e-sports, that dungeon crawls turn into speed runs, and players employ clever uses of game mechanics.
Player vs player conflict can also conjure immense emotions such as fiero and agony, which make lasting impressions in memory.
I consider Go, TF2, and Aion to all contain direct, explicit player competition. PvP is a broad category. However, there is clearly a distinction between Battlefield 3 matches and PvP in EVE. It boils down to fairness. Games of StarCraft begin and end; each player starts at a strategically balanced state; and it is through the game rules that deviations occur in power until one player succumbs and is defeated.
PvP in an MMO, specifically "world PvP", is inherently unfair. One or more players have an objective, quantifiable advantage over others. One side will have higher levels, better gear, or more participants. Any game with persistent character progression will have this imbalance manifest. A fair fight can occur coincidentally, but it is certainly not something to be expected.
MMO PvP happens within a larger context, thus world PvP transforms into more than a simple combat affair between two parties. PvP starts as soon as the player logs in. Events preceding the actual engagement ripple through the world and can affect fights. Actions that happen before, after, and during combat make world PvP an unbounded arena spatially and temporally. Without borders, players scout, hunt, run, hide, and most importantly are vulnerable before and after the actual combat.
A simple analogy: Fair PvP is a cock fight, and world PvP is the African Savannah.

World PvP requires players to be mindful of the environment. Not just navigable terrain, safe spots, and avenues of retreat, but also the entire possibility space of events. Does the enemy have backup? How many? How long until they arrive? What are my chances?
This is clearly an all-encompassing mindset of playing. It is more than action-oriented twitch combat, and more than efficient resource management; it is expecting the unexpected through planning and preparation. World PvP is an expectation in the minds of players.
Different mechanics can be layered on top of that expectation to change the level of risk and consequences, and thus the intensity of emotion the game provides. There are also many forms and implementations of world PvP.
I did a very brief and informal survey--"What is world pvp?". These were some of the answers:
unrestricted warfarebeing able to pvp throughout the entire "game world"you walking around and someone ganks youusing environment to your advantagecooperationunknown, different factors you control, rather than just being fairno rulesnot worth my timewaiting until situation is in your advantage
What is world PvP to you?
This weekend was wholly uneventful in EVE which is 100% my own fault. EVE requires players to actively engage it, and that's what I did tonight. I convinced myself to pick a fight (and most likely lose it). There is no use sitting on all this ISK if I'm not going to spend it.