Plain English Meaning
Before flying an aircraft you haven't flown before, an instructor takes you through how that specific airplane works on the ground and in the air, then signs you off once you can handle it competently.
Full Definition
A structured process in which a pilot, already certificated to fly a category and class of aircraft, receives ground and flight instruction in a specific make and model in order to demonstrate the knowledge and skill required to operate it safely. Checkouts are typically conducted by a flight instructor or by an instructor designated by a flight school, rental operator, club, or insurance carrier, and conclude with the instructor's logbook endorsement or a written record stating is to act as of that aircraft.