It's the Rod of Asclepius, not to be confused with the caduceus!

There are various theories why this symbol was invented. The one that makes most sense to me is that it depicts a (formerly widespread) parasitic nematode being removed by wrapping it around a stick to slowly draw it out of the body.

For a visual demonstration of the parasite and its removal: Bizarre Beasts - When is extinction the 'right' choice?