A common type of exploit deals with pathing issues. In some games it is possible to maneuver a Boss mob into a position where he gets stuck in the geometry, unable to move. Then you just stand back and slowly destroy him at a safe distance. While this may seem smart playing, it is considered an exploit and can get you in trouble.
Use of exploits is almost universally frowned upon and, in most games, if you get caught using one repeatedly rather than reporting it as an error, and the devs find out, it will get you banned (or at least they will take away whatever you gained by using it). Entire Guilds have been banned from many games, including WoW and EverQuest II, for farming an exploit.