There are a few things that come into the physics of punching something. First off, impulse plays a huge role in punching somehting. Obviously as you punch something such as a wall or a person you will experience an impulse as you have a change in momentum. Therefore the thing that you are punching will feel the force of the punch as well as the impulse delivered from the punch. Due to Newton's second law you, the puncher, will also feel a force driving backwards in your direction as every reaction has an equal and opposite reaction. This describes the physics of punching something with your fist.