Plain English Meaning
A signed note from a flight instructor that gives a student pilot permission to fly a specific type of airplane alone. Without it, a student is not legally allowed to fly solo.
Full Definition
A written authorization signed by an authorized flight instructor in a student pilot's logbook (and on the student pilot certificate, where applicable) that permits the student to act as pilot in command of a specific aircraft without an instructor on board. The endorsement is required by 14 CFR Part 61, must specify the make and model of aircraft, and is valid for a limited period (typically 90 days) before it must be renewed by an instructor who has flown with the student.