Plain English Meaning
When ATC clears you somewhere, they have already worked out a safe distance between you and everything else in the sky. Clearance separations are the rules that decide how much space that has to be.
Full Definition
The minimum spacing that air traffic control must maintain between an IFR aircraft and other aircraft, terrain, obstructions, and certain types of airspace when issuing a clearance. ATC applies these standards vertically, laterally, and longitudinally so that two aircraft cannot legally occupy the same block of protected airspace at the same time.
Context Anchor
Seen when studying IFR clearances and how air traffic control keeps aircraft separated during departures, arrivals, , and .