Plain English Meaning
It's the direct, diagonal distance from your aircraft to a station on the ground — not the distance across the ground beneath you. The higher you are or the closer you get, the more the diagonal stretches beyond the true ground distance.
Full Definition
Slant range is the straight-line distance from the aircraft directly to a ground-based navigation station, measured along the line of sight rather than along the ground. Because this line is the hypotenuse of a triangle formed by the aircraft's altitude and its horizontal distance from the station, slant range is always greater than the actual ground distance, with the error increasing as the aircraft flies higher or closer to the station.
Context Anchor
Seen in instrument flying when using distance measuring equipment, especially in discussions of why the indicated distance can be slightly wrong near a station.
Derivation
‘Slant’ comes from an old Scandinavian word meaning to lean or tilt, and ‘range’ means distance. Together they a distance measured along a tilted line — exactly what a signal travels from the aircraft down to the station.