The second law of motion, F=ma=mv/t is applied here.When an athlete of mass m jumps from a height h he strikes the ground with a velocity v, thus his momentum just before striking is mv. Now after hitting the ground he comes to rest, thus his momentum changes from mv to 0. If he is allowed to fall on a hard surface he comes to rest quickly in small time t, thus force acting on him becomes large and he gets hurt. (F = mv/t, if t is small F becomes large)
If he is allowed to fall on a cushion or sand bed, the sand slowly drifts away under him and gives him more time to stop. . (F = mv/t, if t is large F becomes small) This lets him experience less force and thus he does not feel much pain.