Plain English Meaning
An approach that gives you a radio beam to keep you lined up with the runway, plus a distance readout telling you how far you are from a fixed point. You use the distance to know when to step down to lower altitudes, because there's no electronic up-and-down guidance.
Full Definition
An instrument approach procedure that uses a localizer for lateral (left/right) guidance to the runway, paired with DME to provide continuous slant-range distance information from a designated DME station. Unlike a full ILS, a LOC/DME approach provides no electronic glideslope, so it is flown as a non-precision approach using step-down altitudes referenced to DME distances.