I think GP means that if you are stationary relative to the ground (such as on a space elevator or a rocket going straight up), 35786 km up is the only height

I think GP means that if you are stationary relative to the ground (such as on a space elevator or a rocket going straight up), 35786 km up is the only height which is a stable orbit. If you let go of the elevator too early, you'll fall to the ground; too high and you'll fly off into space.