In Numbers 21, as the Israelites wandered the desert under the leadership of Moses, they began to complain as they so often did. As punishment for this, the Lord sent serpents amongst the people and many were bitten and died.
When the people finally acknowledged their sin, the Lord gave Moses a command to create a bronze serpent and put it up on a pole. When the people were bitten by a serpent, if they looked upon the bronze serpent they would live.
As a side note, the symbol of the American Medical Association is derived from this story. It is a depiction of a serpent, or pair of serpents depending on the rendition, upon a pole.
Eight hundred years after Moses constructed the bronze serpent to save the Israelites, it was apparently still around and the people were worshipping it by burning incense to it. It is not only Hezekiah becomes king that it is finally destroyed.
2 Kings 18 mentions the destruction of the bronze serpent and notes that it was called Nehushtan. The word Nehushtan sounds similar to both the Hebrew words for bronze and snake so it it is easy to figure how it received its name.