This ties in with body mechanics and using your body weight in conjunction with what you are doing. In order for this to be done at the fullest potential, your timing has to be correct. The idea is to transfer power to the side of the body where you need the power. The key to the power transfer is the hand that is withdrawing, which is coming back in timing with the one going out. It has the same amount of force and power coming back as the punch going out.
All actions require an equal and opposite reaction.
Imagine that you are driving your punch through your opponent. Do not focus on the target, but through the target. I have been an Isshin-Ryu student for over 30 years. But it was only about 10 years ago when I became a student of Sherman Harrill that things started to come together. One of the finest lessons he taught me was do not take anything for granted.