[Daffynition]

One of the earliest [western] Caduceus that I have encountered is found at the Asklepion, Bergama (Pergamum) ... the snakes, the symbol for Aesklepios, ornament the marble altar. In the ancient world, snakes symbolized healing and life-renewal. The caduceus was adopted as a symbol of the medical profession because of its similarity with the serpent entwined staff of Aesklepios.

[TexasNative2000]

The caduceus was adopted as a symbol of the medical profession because of its similarity with the serpent entwined staff of Aesklepios.

That symbol is also based on God's command to Moses to wrap a snake on his staff and hold it aloft to heal his people.