To push an ally out of cover when being pinned by suppressive fire in an FPS.
Etymology: The word is a reference to a "Call of Duty: Modern Warfare" character known as Gaz, whose AI is infamous for pushing the player out of cover during the game's "Campaign" mode.
Person A: I need some cover! they're cappin' the hell outta us!"
Person B: Hey! Quit pushin! Don't Gaz me Bro! Your GAZZING me!