Plain English Meaning
A radio system that tells the pilot how many nautical miles the aircraft is from a specific ground station. The aircraft sends a signal, the ground station answers, and the equipment turns the round-trip time into a distance shown on a display.
Full Definition
An airborne and ground-based radio navigation system that measures the slant-range distance in nautical miles between an aircraft and a fixed ground station. The aircraft's DME interrogator sends paired pulses to the ground transponder, which replies on a different frequency; the equipment calculates the time between transmission and reply and converts it into a distance reading displayed in the cockpit.