It originates from the posterior cord of the brachial plexus, and continues down the arm staying posterior. Going down the humerus, the radial nerve travels goes through the radial groove on this bone.
The radial nerve and its braches supply the dorsal muscles, such as triceps brachii, the extrinsic extensors of the wrist and hands, and the cutaneous nerve supply to most of the back of the hand. (The ulnar nerve cutaneously innervates the back of the little finger.)
The radial nerve divides into a deep branch, (which becomes the posterior interosseous nerve), and continues as the superficial branch which goes on to innervate the dorsum (back) of the hand.