Plain English Meaning
DME has two parts that work together: a radio in your aircraft that asks 'how far am I?' and a radio on the ground that answers. The aircraft times how long the round trip takes and turns that into a distance reading on your instrument panel.
Full Definition
The two pieces of equipment that make a Distance Measuring Equipment (DME) system work: an airborne interrogator installed in the aircraft, and a ground-based transponder located at a navigation facility such as a VOR or ILS. The interrogator sends paired pulses on a UHF frequency; the ground transponder receives them and replies with its own paired pulses on a different UHF frequency. The aircraft equipment measures the round-trip time of the signals and converts it into in , which is displayed in the along with and .