Answer to that we can find in Chinese traditional medicine. According to it our body (as everything else in the nature) has its balance of Yin and Yang. Diseases disrupt that balance. For example it is believed that if you suffer from rheumatism your body is drained from Yang (sun, active) energy. Thus, to feel better you need to 'supplement' it. Apparently alcoholic beverages have power to do just so (which isn't far from truth since alcohol, drank in small amounts, can improve blood circulation, making us feel more 'active' or invigorated). That is why medical wine has been in use since ancient times. To make it more potent people tend to add various herbs, fruit and yes... snakes.
Apparently it does matter what kind of snake you're using (the more venomous the better). It's believed that snakes bring vitality. That is why they're thrown into jars with the rice wine to soak for a few months (the procedure dated as far as 700 hundred years BC). Afterwards the 'essence' of the snake venom should dissolve in the potion. Here you might wonder if it won't be dangerous to drink it. Well - not really. The venom is made of proteins which tend to denature in contact with ethanol. In other words – they loose their properties. There is however one thing to be cautious about. While the venom loses its 'bite' after few months of soaking in the jar, the snake itself might not. There have been reported cases of snake bites after opening the jar. Apparently some snakes survived by getting into hibernation state (although it's a very rare occurrence).
One thing to add here is that not only snakes can be a source of invigorating energy. Basically anything venomous goes: scorpions, Chinese red-headed centipedes (which, to my horror, creep through the Zhejiang woods), even wasps or hornets. All together things that make a shop look like a hoot of the evil witch.
So what do those potions suppose to cure? Nearly anything. But main claims are about kidney diseases, anemia, rheumatism and cold. Any scientific proof for that? None. At least nothing more than a shot of any regular alcohol would do.