Let’s keep in mind where we are in the context of this scene. Earlier in the desert journey, the Israelites had complained of lack of food and water. The Lord had responded with gifts of quail (Numbers 11:31) and manna (Exodus 16; cf. Numbers 11:6), and with water (Exodus 17; cf. Numbers 20:11). So even though the Lord supplied them with the bare necessities, they now start to complain about the “taste” of the food, protesting loudly that they were “sick of this unsatisfying food.” There is an old saying, “never bite the hand that feeds you”; and now as a result of their whining behaviour (a conclusion they reach in hindsight), they find themselves being bitten and killed by poisonous snakes.
They presume that the misfortune was caused by the sin they had committed in complaining about the provisions God had made for their journey in the wilderness. So, they asked Moses to intercede with God to remove the cause of their death. God did not do this; but he gave them a way to be healed of the bites that caused the terminal illness: If anyone is bitten and looks at it he shall live. It is assumed (but not written here), that when they look upon the item raised on the cross, repent of their sinfulness, and believe in God, they would be healed. It is not “magic”; it is not make-believe; it is faith-based and prophetic.
Jesus saw this story in the Book of Numbers as a “prediction” of something that would be accomplished and fulfilled in his own life. He points out this fact in the gospel today (John 3:13-17) when he tells Nicodemus that anyone who looks at Him (the Son of Man) “lifted up,” believes, and repents, will receive a healing that lasts for all eternity!
In the Old Testament, God permitted the making of images, such as the bronze serpent, that pointed symbolically toward salvation by the incarnate Word. The story of the bronze serpent is a “type” or predicting the saving act of Jesus Christ on the Cross.
Also see articles #2130, and #128 in the Catechism of the Catholic Church.