In boxing and martial arts hook punches (also known as "hooks") are either offensive (when they are thrown from the back arm) or defensive (when they are thrown from the lead arm).  

What's involved: Shoulders, quads, calves, hips, lateral abdominals. 

Powered by: Core and hips. Whether performed from the lead arm or the back one you need to twist your body in time with the punch. 

Tip: As you punch, bring your elbow up so that it is parallel to the floor and you have a ninety degree angle at the elbow joint. Then twist on your feet, using your hips to throw your body behind the punch.