The symbol in this image is called a “caduceus”.
The caduceus consists of two snakes, wrapped around a center rod, with two wings attached to the rod above the snakes.
The caduceus is the symbol for the medical profession. There are various theories as to why the caduceus is the symbol for the medical profession. The real reason the caduceus symbol represents the medical profession is because the caduceus is a representation of a human body. How it represents the human body is easy to see.
The human body has two sides.
There are two snakes wrapped around the caduceus.
One to the right of the center rod,
and one to the left of the center rod.
It seems obvious that the right snake represents the right side of the body,
while the left snake represents the left side of the body.
That leaves the center support of the caduceus unaccounted for.
That is an easily rectified situation. The human skeleton,
includes a spine with a skull on top.
The outline of the spine and skull looks just like the center rod of the caduceus.