1. vi. To destroy utterly. Like frag, but much more violent and final. "There's no trace left. You definitely gibbed that bug". 2. n. Remnants after total obliteration.
Originated first by id software in the game Quake. It's short for giblets (thus pronounced "jib"), and referred to the bloody remains of slain opponents. Eventually the word was verbed, and leaked into general usage afterward.