Some people have erroneously stated that it has to do with shielding the subject from the hammer's momentum. This is not the case. Every bit of momentum imparted to the smashed object by the hammer is imparted to the person and subsequently into the earth that supports him. If the hammer hit the body directly then all the force of the hammer would be concentrated on a small area in a short amount of time and the hammer would do a lot of damage to the person's body. So the idea is to protect the person by spreading the impact over as large an area as possible and over a large amount of time.
Kinetic energy is the energy of motion.
When physicists analyze momentum they think about the time during which forces act, but when they analyze energy they think about the distance through which forces act. This is because the energy a body acquires is equal to force multiplied by the distance over which the force pushes the body. During the hammer's impact with the stone, the stone moves through a smaller distance than the hammer. Equal forces but unequal distances result in unequal changes in kinetic energy. The hammer loses more kinetic energy than the stone gains.