Plain English Meaning
The book that comes with the airplane and tells you exactly how to operate that specific airplane safely -- its limits, its procedures, and its numbers.
Full Definition
The official document, produced by the airplane manufacturer and approved by the FAA, that contains the operating limitations, procedures, performance data, weight and balance information, and systems descriptions specific to a particular airplane. The Airplane Flight Manual (AFM) is the FAA-approved manual required to be carried in the aircraft; the Pilot's Operating Handbook (POH) is the manufacturer's expanded version that, for most modern light aircraft, is also the AFM. The two terms are commonly written together as AFM/POH because for a given airplane they typically refer to the same document.