Can you translate this for someone who's never played MMOs before?
Are you talking about people who join a faction and attack members of their own team?
Griefers are basically the lowest possible rung of people in an online game, who go out of their way to deliberately ruin the experience for other players. I remember playing in a beta years ago, there was a whole in-game guild of people who shared each other's account info and scheduled leveling, basically so that somebody was grinding the character 24/7, and not surprisingly they tended to have more high-level characters faster than anyone else. They did not participate in events, boss hunts, or other high-level game content. They used their advantage to bother other players, camping at the borders of PvP zones to kill anyone of any faction who was just passing through, and ran around using large area-effect abilities to wipe out all the enemies in low-level grinding areas. The enemies were too weak to provide them any benefit at all; they were just going out of their way to keep any new players from being able to actually play. Griefing appears in any multiplayer game, like Left 4 Dead, which revolves around a small team of 4 who rely on each other. Sometimes people will join the game and immediately kill teammates or themselves, leaving that game pretty much dead in the water and forcing players to try and join a new one. That's griefing, playing the game with the sole intent of making it less fun for others.
EVE Online's player-centric setup has advantages unique from other MMO's, but its weakness is that it's subsequently far more vulnerable to griefing. In EVE, players are behind pretty much everything; if you buy something in a store, it was likely made by a player, who probably made it from materials mined by other players. Enormous factions control equally enormous territories in space, own and built the space stations you visit, control security in the area, etc. Griefers are everywhere, though, because of the fact that players have relatively free reign to do whatever they want. So you constantly have to deal with people camping warp gates and indiscriminately targeting everyone, entering low-grade systems with high-end ships and strip mining them, despite this being far less profitable than other systems, just so that the weaker players have to wait for respawn, only to likely have it stolen again.
That's the fear with the player-centric system that CCP is aiming for with WoD. As soon as the players are given power, griefers are going to abuse it.