Numbers 21:6-9 (NIV)
6 Then the LORD sent venomous snakes among them; they bit the people and many Israelites died. 7 The people came to Moses and said, “We sinned when we spoke against the LORD and against you. Pray that the LORD will take the snakes away from us.” So Moses prayed for the people.
8 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.” 9 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, they lived.
I believe the key here is the type of action that was taken "raising up" and the result of that action "healing". If you recall the people of Israel were struck with a plague of snakes. To alleviate the plague Moses was instructed to raise up a bronze snake and all who looked at the snake were healed.
14 Just as Moses lifted up the snake in the wilderness, so the Son of Man must be lifted up, 15 that everyone who believes may have eternal life in him.”
We are bitten with a plague of sin, Christ was raised up on the Cross. Those who look to Christ are healed. I also don't think its a coincidence that the plague was snakes. This goes back to more snake imagery involving Jesus from Genesis:
15 And I will put enmity
between you and the woman,
and between your offspring and hers;
he will crush your head,
and you will strike his heel.”
Jesus' coming was foreshadowed with snakes as far back as Genesis, this is a continuation of that theme.