Plain English Meaning
It is the aircraft's main onboard computer for flying the planned route. The pilot enters the route, and the system figures out where the aircraft is, where it should go next, and how to get there, then feeds that information to the autopilot and the cockpit displays.
Full Definition
A Flight Management System is an integrated airborne computer system that automates a wide range of in-flight tasks, including navigation, flight planning, performance management, and guidance of the aircraft along a programmed route. It combines inputs from multiple navigation sources (such as GPS, inertial reference systems, and -based aids), uses an internal of , , airports, and , and provides outputs to the autopilot, , and cockpit displays so the aircraft can fly a preprogrammed route accurately and efficiently.