"The Lord said to Moses, “Make a snake and put it up on a pole; anyone who is bitten can look at it and live.” So Moses made a bronze snake and put it up on a pole. Then when anyone was bitten by a snake and looked at the bronze snake, he lived."
All who were bitten by snakes and so were afflicted by their venom needed only to look upon the image of their affliction, a brazen snake, and they lived. It does not say they had no adverse reaction to the poison in their veins, but merely that they lived. And the symbolism of the Snake is still used today as a symbol of healing because of this.
However snakes carry a deeper meaning in the Bible. It is the creature who is accursed above all other creatures. The bronze snake is the very image of sin though harmless in and of itself. Likewise has Christ, pure and holy, become the image of sin so that all who look upon him might live. Whereas all who looked upon the bronze snake lived despite the venom, so all who look upon Christ will live despite all their sin!
Seeing Christ as he truly is, namely as the risen Son of God, has a deep transformative impact on all who behold him. Look to the Son of God, the only risen Son, and you will live, no longer afflicted eternally but only temporarily. The poison will pass and by the grace of God we will endure.