Short Answer
A grudge monster is a creature created by the GM as an avatar by which to inflict their wrath upon a player. (From tabletop RPG terminology, presumed to orginate with Dungeons and Dragons.)
Longer Answer
A tabletop roleplaying game is like a computer-based RPG, but with an actual human telling the story and managing the game mechanics in place of the computer (fancy that!). The important difference, for our purposes here, is that machines are impartial and humans are not. This means that, although the players and the game master are supposed to keep their real lives and feelings entirely separate from events in the game, they often do not. This has caused many people a great deal of grief.
The game master is in the unique position of controlling everything in the world besides the player characters. Doing so in a lively and believable manner requires imaginative storytelling, which is a very personal and human process; therefore the game world is inescapably subject to the GM's personal judgement. It's impossible by definition for the GM to cheat, since they make the rules (and the GM's ruling always trumps any rulebook a player can produce). But while it is occasionally appropriate to fudge a dice roll or produce a "random" encounter to maintain the right challenge level and keep the game on an even keel, a seriously cheesed off GM might be tempted to assert their power in a more punitive fashion. Players have been known to have their characters attack each other based on personal grudges; what do you think happens if a player insists on annoying the GM with rules lawyering, or constantly whines about the progress of the campaign, or contests every turn of the dice?
"A dragon eats you."
Problem solved.
For further illustration, see Real Life (the webcomic) for 31 July and 2 August of 2000.