Final answer:
The thoracodorsal nerve arises from the posterior cord of the brachial plexus and innervates the latissimus dorsi muscle.
Step-by-step explanation:
The nerve that arises from the posterior cord of the brachial plexus and runs along the medial surface of the latissimus dorsi muscle, which it innervates, is the thoracodorsal nerve.
This nerve is responsible for the motor innervation of the latissimus dorsi muscle, which is used in movements such as pulling, climbing, and swimming.