The image which you see below is called the Caduceus, it comes from the ancient Roman mythology and it was the magic wand of the God Mercury who could control the living and the death with it. The snake was an ancient symbol of health because it could shed its skin and look young again.
The practice of medicine is one of the oldest professions in history of mankind, some of those practices still applied today in modern healthcare, such practices were originated from hundred or even thousands of years ago most notably from the Hun dynasty