Plain English Meaning
The part of the engine that makes electricity has stopped working. The aircraft is now running on battery power only, and that battery will eventually run down.
Full Definition
A condition in which the engine-driven generator stops producing electrical power, leaving the aircraft's electrical system dependent on the battery alone. Once the generator fails, the battery is no longer being recharged in flight and will deplete over time, progressively losing power to radios, instruments, lights, and other electrical equipment.
Context Anchor
Seen in instrument flying discussions, emergency checklists, and cockpit warning indications for electrical system problems.
Derivation
Generator comes from the Latin idea of “bringing forth” or “producing.” In , it means a device that produces electrical power for the aircraft while the engine is running.