Plain English Meaning
DME tells the pilot how far the aircraft is, in nautical miles, from a chosen ground station. It does this by sending out radio pulses, timing how long the reply takes to come back, and turning that time into a distance.
Full Definition
The role of Distance Measuring Equipment (DME) in providing the pilot with a continuous, accurate readout of slant-range distance in nautical miles from the aircraft to a selected ground station. The airborne DME unit transmits paired pulses to the ground station, which replies on a separate frequency; the unit measures the time between transmission and reply and converts it to distance, typically also displaying groundspeed and time-to-station along the .