I would like to know the meaning for God's command to Moses to lift a serpent of brass and set it on a pole in the desert, so that all those who had been bitten by serpents would look at the brass serpent on the pole, be cured and live.
The Mishnah (Rosh Hashanah 3:8, cited in Rashi to this verse) states:
"Does a snake kill or make live? But rather, this tells us that as long as the Jews looked upward and subjugated their hearts to their Father in Heaven - they would be cured; if not, they would decline."
Ibn Ezra comments that we can't know why G-d specifically told Moshe to make a figure of a snake rather than something else; it was a Divine command beyond our understanding.
Nonetheless, other commentaries do offer possible reasons:
It demonstrates G-d's power: the same snake that He gave the power to kill people with its venom, is the same one whose depiction will be the instrument of their healing. (Daas Zekeinim; Ramban)
It would remind the Jewish People of the sin they committed by speaking slanderously of G-d and of Moshe (the snake is a symbol of slander, as in the episode of the Tree of Knowledge, where he falsely claimed that G-d didn't want Adam and Chavah to eat from it because He didn't want competition - Gen. 3:6), so that they would repent properly. (Sforno; Ohr Hachayim, who also provides seven other benefits that they'd get from looking at this copper snake and considering its implied message)
It would remind them of the instrument by which they had already been punished. This is similar to a father who once had to beat his child, who afterwards hangs the rod on a wall as a reminder to his son to not repeat the act that led to its use. (Baal Haturim)
- and I'm sure there are many other possibilities that have been offered, since the Torah's "measure is longer than the earth, and wider than the very ocean" (Job 11:9).
I believe the serpent represented their sin, looking up in obedience meant acknowledging their sin to be healed.