[Jewbacca]

I would presume the snakes are from the Exodous story of G-d healing people who looked at the curled bronze snake staff of Moses.

[TomOnTheRun]

Not exactly. It was probably purely pagan in origin. It's association with healing came long long after the the symbol had already been around. Hermes was originally a god of commerce ... he didn't become associate with healing until much much later.

There is a different name for the staff you mention ... I can't remember it now. I only know about the caduceus because I've used it in artwork I've made for a doctor's office. Wish I could help more.