The brachioradialis reflex (also known as supinator reflex http://www.medilexicon.com/medicaldictionary.php?t=46267)is observed during a neurological exam by striking the brachioradialis tendon (at its insertion at the base of the wrist into the radial styloid process (radial side of wrist around 4 inches proximal to base of thumb)) directly with a hammer when the patient's arm is relaxing. This reflex is caused by the Radial nerve C5,C6 spinal nerve.

The reflex should cause slight wrist extension and/or radial deviation, supination

Supination

Supination is a position of either the forearm or foot; in the forearm when the palm faces anteriorly, or faces up . Supination in the foot occurs when a person appears "bow-legged" with their weight supported primarily on the anterior of their feet.The hand is supine in the anatomical position...

and slight elbow flexion.