Plain English Meaning
A route that goes directly from point to point instead of following the standard charted highways in the sky. ATC has to approve it, and you usually need GPS or radar coverage to fly it.
Full Definition
IFR routes flown outside the published Federal airway system, navigated using direct courses between waypoints, fixes, navaids, or RNAV points rather than along charted Victor or Jet airways. Off-airway routes require ATC clearance and are typically flown under radar coverage or with approved area navigation equipment.