Doing something to a player (in a video game) that he/she cannot get out of through means provided by the game's design.
This does not involve emotional things, such as butthurt, as they are psychological issues that are brought up by the individuals themselves and can be caused by anything.
Camping and ganking are often considered griefing by ignorant people and also are called grieifing by thin skinned people who cannot deal with what is involved in playing a particular game or ruleset provided by a game.
"A player griefed a carebear by exploiting the game's system. The player was able to teleport to wherever the carebear was and could not be attacked or targeted."
"Joe Bob hacked the game and found personal information and is now griefing a targeted player with it."