במדבר כא,ט : וַיַעַש מֹּשֶּה נְחַש נְחֹּשֶּת, וַיְשִמֵהוּ עַל -הַנֵס; וְהָיָה, אִם-נָשַךְ הַנָחָש אֶּת-אִיש --וְהִבִיט אֶּל -נְחַש הַנְחֹּשֶּת, וָחָי
The Jews were guilty of Lashon haRa, slander, a transgression traditionally attributed to the serpent. Slander consumes the victim, it burns just like these fiery serpents burned and consumed the people.
Sforno states that the fashioning of the brass serpent and placing it on a banner, aroused the Jews to examine their sin, bringing them to repentance. This was the purpose of the staff of serpents. It was a means to an end, not some magical cure.
Moshe originally thought to make the staff of gold, because any artifact to be fashioned at the command of HaShem deserves to be made of the most expensive and precious material (like the vessels of the Mishkan).
However, in this case the staff was made of brass since the intention was to underscore the link between נחשת (brass) forged through fire and נחש (serpent) whose venom burns and destroys like slander. This play on words is most instructive.
