**Core Concept**
The median nerve is a mixed nerve that plays a crucial role in the innervation of the upper limb, particularly in the hand. It arises from the brachial plexus and traverses the wrist to supply the thenar muscles, thumb, and index and middle fingers.

**Why the Correct Answer is Right**
The median nerve is responsible for the motor innervation of the thenar muscles, including the opponens pollicis, abductor pollicis brevis, and flexor pollicis brevis. It also provides sensory innervation to the palmar surface of the thumb, index finger, middle finger, and half of the ring finger. This is due to the presence of large numbers of myelinated fibers in the nerve, making it a vital component of hand function.

**Why Each Wrong Option is Incorrect**
**Option A:** Median nerve does not innervate the intrinsic muscles of the foot. The intrinsic muscles of the foot are innervated by the posterior tibial nerve.
**Option B:** Median nerve does not traverse the elbow joint. The median nerve passes through the cubital tunnel at the elbow but does not traverse the joint itself.
**Option C:** Median nerve does not supply the posterior arm. The posterior arm is supplied by the radial nerve.

**Clinical Pearl / High-Yield Fact**
The median nerve is often compressed at the wrist, leading to carpal tunnel syndrome, a common condition characterized by numbness, tingling, and weakness in the hand. This condition can be exacerbated by repetitive hand movements, pregnancy, and certain medical conditions.

**Correct Answer: D. Median nerve supplies the thenar muscles.**