The FAA website predicts pre-flight whether RAIM will be available
The RAIM algorithm will tell you during your flight if GPS is working correctly.
The pre-flight FAA website check is not a substitute for the use of the RAIM function during flight. It will only show whether the RAIM function is available during flight.
RAIM stands for Receiver Autonomous Integrity Monitor. It is a part of aviation graded GPS receivers that checks consistency of all used GPS satellite signals in order to raise an alert if the GPS system is not working correctly.
For RAIM to work, there must be at least 5 usable satellites in view of the GPS receiver. For GPS without RAIM, at least 4 satellites are needed. If there are only 4 satellites visible, or more than 5 but with an unfavourable geometry, RAIM cannot work and therefore the GPS receiver cannot be certain that the produce position fix is correct.
The FAA website predicts the availability of RAIM; based on the constellation of GPS and the health status of its satellites, the route and the time of flight it is possible to calculate whether RAIM is available for your flight. This can be done before you take-off.
If there is no RAIM available during part of your flight, you can't rely on GPS during that part. The GPS may still work fine, but there is no way to check its integrity. A single fault in a GPS satellite or, more likely, a corruption in the downlinked GPS satellite almanac will cause the position fix to be off. You must use alternative navigation means if GPS RAIM is not available.
The FAA website does not say anything about the actual quality of the GPS system during your flight. This is what RAIM does. It continuously monitors all satellite signals for consistency and flags any inconsistencies. There are various categories of RAIM such as Fault Detection and Fault Detection & Exclusion but all RAIM algorithms will give you a containment radius.
The containment radius is the maximum size that a position error can grow due to a fault in the GPS system without the RAIM algorithm being able to detect it. The value of the containment radius depends on the geometry of the satellites.
The requirements for the value of the containment radius depend on the flight phase. For En-Route mode the RAIM containment radius value should be under 2 NM, terminal mode under 1 NM, and approach mode 0.3 NM.