The image of serpents wrapped around a staff is a familiar one in the medical field, decorating hospitals, pharmacies, and pharmaceutical products. The stick is actually a staff that was used by the Olympian god Hermes. In Greek mythology, Hermes was a messenger between the gods and humans – which accounts for the wings, and a guide to the underworld -which explains the staff.
Hermes was also the guardian of travelers, which makes his connection to medicine appropriate because, in the olden days, doctors had to travel great distances by foot in order to visit their patients.
Hermes was apparently given the staff by Apollo, the god of healing and it is entwined with two white ribbons. The ribbons were later replaced by serpents, as one story tells that Hermes used the stick to separate two fighting snakes who then coiled around his staff and remained there in balanced harmony.