Plain English Meaning
A flight that goes straight from one point to another instead of following the published highway-like routes in the sky. ATC has to approve it, and the aircraft usually needs GPS or similar navigation gear to fly it accurately.
Full Definition
IFR flights conducted along a route that is not defined by published airways, but instead proceeds directly between fixes, navaids, waypoints, or coordinates as filed and approved by ATC. Direct route flights may be flown using area navigation (RNAV) equipment, between VOR or other navaid radials, or as a straight line between two named points, provided the aircraft remains within coverage or meets equipment requirements for - navigation.