When you are driving and put an automatic vehicle in neutral why do the RPMS stay higher than idle?

This is the PCM (Powertrain Control Module) keeping the vehicle prepared for its shift back into gear. If the vehicle detects motion (by VSS signal or ABS Signal) it will keep the engine's RPM's Higher than normal to achive a smooth transition into gear rather than jerking or lurching the vehicle. This prevents damage to the transmission, and typically provides a smoother ride.