Official Aviation Definition
A Flight Management System (FMS) is an integrated onboard computer system that automates a wide variety of in-flight tasks. The FMS manages the navigation database, computes optimal vertical and lateral flight paths, guides the autopilot, and calculates fuel burn and arrival estimates.
In Simple Words
The central navigation computer of a modern jet where pilots enter their flight plan and waypoints.
Real-World Flight Example
Prior to pushback, the first officer cross-checked the gross weight, cost index, and departure route programmed into the FMS.