A 'Power Gamer' is a player who prefers very high powered characters, with super weapons or destructive spells. They will use the rules to get the maxiumum powers that they can, using the letter of the rules even where it conflicts with the spirit.
A small ammount of power gaming is normal for many players, and is not a problem, but some players seem to think that getting the deadliest character, regardless of the plot or the other players, is the point of roleplaying.
Some systems are commonly seen to favour power gaming, especially superhero games and Amber.