The Jews complain about their food, claiming to be disgusted by the manna that they have been receiving. In response, G-d sends snakes to attack them, followed by Moshe’s prayers on their behalf, and instructions to gaze upon a copper snake [nachash nechoshet] to heal them from the snake bites (21:9). Why would looking at a snake be the cure for being bitten, and why was the cure made specifically out of copper?
Rav Dessler suggests that having an elevated statue to which people can look up has the added purpose of reminding the people to look to heaven [G-d] for guidance, a concept that would serve them well. Rav S. R. Hirsch adds that it was made of copper because copper [nechoshet] sounds like a snake [nachash], and further helps remind people to always be mindful [lenachesh – to sense] of the source and purpose of what they have.
As the inevitable entry into the promised land draws near, G-d is trying to prepare the people (and us) to be mindful of the higher purpose, despite the entrenchment of everyday life.