From a Q&A column in the Arizona Star:

Question: What is the origin and meaning of the caduceus, the winged staff and entwined snakes that is the symbol of the medical profession?
Answer: It is not the caduceus, but the staff of Asclepius that is the symbol of the American Medical Association and many other professional medical groups.
For many years, the staff of Asclepius has been confused with the caduceus, a symbol that generally features two snakes encircling a rod topped with wings. According to mythology, the caduceus represents the wand of the Greek god Hermes and is associated with commercial endeavors.
The single snake of the staff of Asclepius is a symbol dating to antiquity, and represents its namesake, the Greek god of healing. In the biblical book Exodus, Moses is told to erect a brass pole with a serpent. Whoever looked upon it was healed.

That last bit doesn't quite fit, but it is usually appended to such discussions somewhere. A reasonably good webpage with some good images of the staff and caduceus ...