Hygieia was a minor goddess in Greek mythology, but her name survives today in the word "hygiene."
In some versions of her story, she is the daughter of Asclepius, the god of medicine, and in others she is his sister or his wife. Her sister is Panacea.
Hygieia was generally celebrated along with Asclepius as a giver of health and was sometimes called The Health. Her popularity (and cult following) grew after the oracle of Apollo at Delphi recognized her virtue following the Athenian plagues in the 5th century BCE. She was later also worshipped in Rome.
The snake, in addition to being a sacred symbol of Asclepius, was a sacred symbol of Hygieia.