Plain English Meaning
The aircraft and its crew have been officially cleared to fly in certain ocean airspace where planes must navigate very accurately on their own, because there is no radar to keep them apart.
Full Definition
A formal authorization granted to an aircraft and its operator certifying that the aircraft's navigation equipment, crew training, and operating procedures meet the Minimum Navigation Performance Specifications required to operate in designated MNPS airspace, historically the North Atlantic high-level airspace between flight levels 285 and 420. The approval confirms the aircraft can hold its assigned track precisely enough to maintain safe lateral separation from other aircraft on parallel oceanic tracks without radar coverage.