Plain English Meaning
How far you stay from the DME station while flying a curved path around it. If the arc radius is 10 NM, you fly a circle around the station keeping the DME reading at 10.
Full Definition
The fixed distance, in nautical miles, from a DME station that defines a curved flight path (a DME arc) around that station. The aircraft flies the arc by maintaining this distance on the DME readout while turning continuously around the station.
Context Anchor
Seen when flying or calculating a DME arc, especially when deciding where to start a turn from the arc toward the next course.
Derivation
Arc comes from Latin arcus, meaning a bow or curve. Radius is Latin for the spoke of a wheel. Together they the spoke-length from the (the DME station) to the curved path you fly.