"Resume Own Navigation" means exactly what it says. The controller was vectoring the aircraft and therefore had responsibility for the aircraft track (including terrain clearance). That responsibilty is being handed back to the pilot.
If an aircraft is off track at this point, the pilot needs more information/instruction to be able to comply.
In NZ, he should either be told "INTERCEPT TRACK" or "DIRECT TO...".
Incidentally, "Direct To" means just that. Sometimes we are asked "is that from our present position?" The question is can you think of any other point in space to start from?
As far as terrain clearance goes, the Radar Controller is still responsible for terrain clearance until the aircraft is re-established on a published track or procedure. Mind you, if you have any doubts about terrain, feel free to ask for confirmation.