Plain English Meaning
The official handbook for a specific airplane. It tells the pilot how to operate that aircraft safely, what its limits are, what to do in an emergency, and how it performs under different conditions. It must usually be carried in the airplane.
Full Definition
The Airplane Flight Manual is the FAA-approved document, prepared by the airplane's manufacturer and specific to that individual aircraft by make, model, and serial number, that contains the operating limitations, performance data, normal and emergency procedures, weight and balance information, and systems descriptions required for the safe operation of that airplane. It is required to be on board the aircraft during for most airplanes.