Jesus refered to what He was going to do, as a fulfillment of the true meaning of the bronze serpent being lifted by Moses in the wilderness (John 3:14-15).
14And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up:
15 That whosoever believeth in him should not perish, but have eternal life. (John 3:14-15)
The Israelites were bitten by venomous snakes and were going to die // all people are 'bitten' by the Serpent and due to sin are going to die (the wages of sin is death)
God provided a way that people could not die due to the snake bites // God provided a way that people can be saved and not die due to their sin
The snakes were the cause of the problem (sin) and the bronze snake was the solution // Jesus was sinless, yet on the cross He was made sin for those that would believe on Him (see 2 Cor. 5:21), baring in Himself their sins
The lifted bronze snake was foolishness for some of the Isrealites, because they couldn't see what good is a statue of a snake when they had actual snake bites (and those died) but those that looked up to it with faith, lived // The cross of Christ is foolishness to those that perish, but to those who look up to it with faith, it is the power of God unto salvation! (see 1 Cor. 1:18)
Due to all those and other similarities, Jesus used the event with the serpent as an illustration, so that Nicodemus (a teacher of Israel, well aware of this event) could understand who Jesus truly was.
In brief the bronze serpent is an Old Testament image of the cross of Christ, and what He bore on it!
However we must be careful to worship Christ and not the cross, because many years after the event in the wilderness, some Isrealites started worshipping the bronze serpent (as an idol), as if it had saved them, when in fact it was God who saved them, using that means. (see 2 Kings 18:4)