Plain English Meaning
The heaviest the aircraft is allowed to be when fully loaded. Add up the airplane itself plus fuel, people, and everything on board — that total must not go over this limit.
Full Definition
The highest total weight at which an aircraft is approved to operate, as specified by the manufacturer in the type certificate and Pilot's Operating Handbook. It includes the empty weight of the aircraft plus everything carried — fuel, oil, pilot, passengers, baggage, and cargo. Operating above this weight is prohibited and renders the aircraft unairworthy.
Context Anchor
Seen in aircraft loading, weight calculations, and the operating limits listed for a specific aircraft.
Derivation
Maximum comes from a Latin word meaning greatest. Gross, in this use, means total before anything is subtracted. Together, the phrase points to the greatest total that is permitted.