Probably an underwhelming answer, but at least on the Rod of Asclepius, the snakes most likely stand for... snakes. Yeah, the ancients could be painfully literal at times. In this case, non-venomous snakes are noted to have been used in the temples of Asclepius for unspecified healing rituals, possibly divination on their guts. Not exactly family-friendly, but neither is most of ancient history.

On the Caduceus, on the other hand, the legend goes that Hermes/Mercury once saw a pair of fighting snakes, and made peace between them using his traveler's rod, so the snakes stand for adversaries finding peace, and for negotiation in general - a suitable symbol for the god of messengers and traders. Over time, however, it got confused with the Rod of Asclepius, so now both are used for medicine... though it does fit the way medicine nowadays is mostly a commercial venture with the occasional health benefit.

Probably an underwhelming answer, but at least on the Rod of Asclepius, the snakes most likely stand for... snakes. Yeah, the ancients could be painfully literal at times. In this case, non-venomous snakes are noted to have been used in the temples of Asclepius for unspecified healing rituals, possibly divination on their guts. Not exactly family-friendly, but neither is most of ancient history.

On the Caduceus, on the other hand, the legend goes that Hermes/Mercury once saw a pair of fighting snakes, and made peace between them, so the snakes stand for adversaries finding peace, and for negotiation in general - a suitable symbol for the god of messengers and traders. Over time, however, it got confused with the Rod of Asclepius, so now both are used for medicine... though it does fit the way medicine nowadays is mostly a commercial venture with the occasional health benefit.