It sounds like putting one’s trust in a totem, but Rashi explains that it is quite different. Quoting the Mishnah (Rosh HaShanah 3:5), he says that it was not the serpent of brass that cured them but when they looked up at it they were reminded of the supremacy of God and submitted themselves to His will.
The Mishnah says, “Could the serpent slay or keep alive? It is rather to teach you that when the Israelites look On High and submit their hearts to their Father in Heaven, they are healed; otherwise they pine away”.
Samson Raphael Hirsch adds, “Happy is he who takes note of the unseen ‘fiery serpents’ that beset his path, put to flight by the Almighty.”
A person’s recovery does not happen by itself. The doctors and nurses play the major role, but the family, the community, religion and one’s own faith and optimism are all crucial.