I've covered this topic before, but the Orthodox Arts Journal has done a better job of it.
(Orthodox Arts Journal) - One of the most surprising images one is faced with considering Orthodox liturgical symbolism is the bishop’s staff sporting two snakes flanking a small cross atop it. Especially in a Protestant North American context, this image seems to hark back to ancient chthonian cults, more a wizard’s magic staff than anything Christian. As I have been doing for other subjects, I would like to take a trip through iconography, through the Bible and other traditions to show how this symbol is all at once thoughtful, powerful and perfectly orthodox in the broadest sense. It also happens to fit nicely with all I have been writing for the OAJ up till now.
The first hurdle we must overcome is the perception that the Western bishop’s staff, the crosier, is really a shepherd’s staff, whereas the Orthodox have this strange snake bearing object. In fact, for a millennia at least, the western crosier was also identified with a serpent as medieval crosiers attest. We could say that there are two basic shapes, the crosier and the “tau” shaped staff which were present in the Church before the Schism, both of these shapes have been interpreted with serpents. The current Orthodox version of the staff with serpents (as seen above with Bishop Vladimir Sokolovsky) is a variation of these models.
We wonder though, how can such an image of serpents, both in the East and West be appropriate for the very symbol of a Bishop’s authority? Many will point to the Biblical story of the bronze serpent, somehow prefiguring Christ, as the basis for this use of serpents on the bishop’s staff. This is a perfectly sound explanation, though it is insufficient to create a complete picture. If we are to look a Moses as the origin of this image, we should look earlier. The very first time we encounter a staff in the Bible, at least a staff that is related to divine authority, is at the burning bush. When Moses doubts the Pharaoh will listen to him, God tells him...
Complete article here.