Plain English Meaning
It is the official handbook for a particular airplane that tells the pilot how to fly it safely, what its limits are, and what to do in normal and emergency situations.
Full Definition
The Airplane Flight Manual is the official document, approved by the FAA and prepared by the airplane manufacturer, that contains the operating limitations, procedures, performance data, and other information required to safely operate a specific airplane. It is aircraft-specific, meaning each individual airplane has its own AFM tied to its serial number and equipment.
Context Anchor
You will see AFM references in FAA handbooks, aircraft checklists, and training discussions when a procedure or limit depends on the specific airplane being flown.