Plain English Meaning
RAIM is the GPS receiver's way of checking its own work. It looks at signals from several satellites and cross-checks them to make sure none of them are lying. If something looks wrong, it tells the pilot the GPS may not be reliable.
Full Definition
A self-checking function built into a GPS receiver that verifies the integrity of the satellite signals it is using for navigation. RAIM compares signals from multiple satellites to detect whether any one of them is providing faulty data. To perform a basic RAIM check, the receiver needs at least five satellites in view (or four plus a barometric altimeter input). If a fault is detected, RAIM warns the pilot that the GPS position cannot be trusted for the current phase of flight.