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A "hack" is a form of cheating that exploits some aspect of the game to grant a user an unfair advantage. Hacks differ from exploits in that hacks are almost never achieved in-game, but usually require an external technique; often a third party program.
The term is commonly used for every sort of in or out-game cheating, and can refer to a cheated character, item, account, or something else. The word "hack" can be combined with the another word to detail the particular type of hack: Account-hack, Char-hack, maphack (a 3rd party program that reveals the entire level map in Diablo 2), etc.
"Hack" can be used as a verb, to describe the process of cheating.
- "My character was hacked."
Or as a noun, to describe the program or technique itself.
- "I used a hack to steal his gold."