Its meaning as shown in the programme was quite fitting. It said: The stick denotes a human body. The snakes are the dual minds that a human has. One snake denotes the negative side that we possess and the other denotes the positive one. Their focus (as in the pic), is on the human body, to make it comply as the minds wish, with which the body has to constantly struggle with. The wings denote the soul which is connected with the body and gets affected by the body’s doings.
Now-a-days, the doctors cure only the ailments of the body. In ancient times, the doctors actually healed the body, mind and soul. And that is the reason this particular symbol is said to be the doctor’s symbol. Quite an interesting and relevant find!