Final answer:
The median nerve innervates the lateral three one-half digits of the palmar surface, including several muscles that allow for the precise movements of the fingers.
Step-by-step explanation:
The nerve that innervates the lateral three one-half digits of the palmar surface is the median nerve. This nerve is responsible for the sensation and movement in the palmar aspect of the thumb, index finger, middle finger, and the lateral half of the ring finger. It also innervates several muscles of the hand, including the thenar muscles, which facilitate the precise movements needed for tasks such as typing and writing. The thenar muscles are the abductor pollicis brevis, opponens pollicis, flexor pollicis brevis, and adductor pollicis.
Additionally, the flexor digitorum superficialis and the flexor digitorum profundus muscles, located in the anterior compartment of the forearm, are also innervated by the median nerve and are essential for flexing the fingers.