Plain English Meaning
Before flying a GPS approach, the receiver checks whether it has enough good satellite signals to trust its own position to approach-level accuracy. If it doesn't, it warns the pilot and the approach can't be used.
Full Definition
A self-checking function inside a GPS receiver that confirms the satellite signals it is using are accurate enough to support an instrument approach. Approach RAIM uses a tighter accuracy tolerance than the RAIM used during enroute or terminal flight, because an approach demands more precise position information. If the receiver cannot verify signal integrity to that approach-level standard, it must the pilot, and the GPS approach cannot legally be flown.