Final answer:
The median nerve branches innervate the hand muscles, including the thumb, index finger, middle finger, and half of the ring finger. It also innervates the forearm muscles that control wrist and finger movements.
Step-by-step explanation:
The median nerve branches innervate the muscles in the hand, specifically the thumb, index finger, middle finger, and half of the ring finger. It also innervates the muscles in the forearm, including the flexor muscles that control movements of the wrist and fingers. The median nerve is responsible for sensory perception in these areas as well.