This is the symbolic representation of Caduceus. It is used by Hermes (Greek God). It comprises a rod with two snakes interwind around it and wings at the top. If you search in the internet, there are many stories related to this symbol, but there is got one that makes sense.
So let’s start with wings, it’s the wings of Dove Bird, which represents peace. In the medical field, peace is very important (and ironically currently it’s missing somewhere). Secondly, that rod represents a human which is surrounded by two serpents, representing positivity and negativity.
Both serpents looking at each other represents balance and concentration. When you are medical, you have to learn to balance both, positivity and negativity, and do your work with high concentration, cause your one incorrect decision can affect someone’s life.
Prophetpedia 