Taking control of another person's character on a role-playing forum or chatroom. Sometimes done by mistake, when a player believes another player's character was doing something they weren't. Can also be used to refer to using out-of-character knowledge (information the player has that their character shouldn't) to gain an in-character advantage, though this is more accurately described with the term metagaming.
Godmodding and godmoding are often mistaken for being the same word or concept. However, godmoding (or power gaming) is, in fact, a separate concept with its own, distinct meaning.
Player A: Alice calls Bob forward, and the moment he steps forward, the trap is sprung, dropping him into the floor below!
Player B: Hey, that's godmodding, I never said Bob stepped forward!
Player B: Bob carefully steps over the trap as he approaches Alice.
Player A: Bob doesn't know there's a trap there! I call godmodding!
Mispelling of Godmoding & God Modding in rpg and forum settings, thus the meaning is the same. The term applies to "Godly-modification" or "Godlike-modification" to a character, through skills such as evasion and the like, as well as the character's personality which usually consists of a superior "I know all, see all, and am all", et cetera. The singlemost annoying and obnoxious gamers on the planet. Tend to act like 7 year olds when they don't get their way during games of pretend, i.e. - Bang, you're dead! Yeah huh, I killed you and you can't play anymore!
Godmodding Bill not only managed to magically know the secret base's true location, but also passed all of the armed guards by hopping from tree to tree like a natural-born monkey, and managing to rewire the electric locks which were state-of-the-art using a paperclip and a piece of fuzz from his pocket. Once inside, Bill used his deadly and artful bare hands (along with a combitionation of poison that he had learned in one week to brew in his toilet) to take down 38 of the guards and dogs, inside. That done, it was a mere task of busting through fifty-eight doors and cartwheeling gracefully through the laser beams, before waltzing into the innermost vault and plucking up the plans for complete world domination.