Plain English Meaning
An A&P is an FAA-licensed aircraft mechanic who is qualified to work on both the body of the aircraft and the engine. When a pilot says "I'll have the A&P look at it," they mean the certified mechanic who maintains the airplane.
Full Definition
A certification issued by the FAA to a mechanic authorized to perform maintenance, preventive maintenance, and alterations on an aircraft's airframe (the structure of the aircraft) and powerplant (the engine and its associated systems). An is qualified to inspect, , and return aircraft to within the limits of their certificate.