God had Bnei Yisrael stare at and contemplate the image of the snake, and then remind themselves that God's power exceeds and can even reverse the powers of venomous snakes.
Parashat Chukat records the incident of the nechash ha-nechoshet, the copper image of a snake that God ordered Moshe to construct to cure those among Benei Yisrael who were bitten by the snakes that ravaged the Israelite camp. God had punished the nation for their complaints against Him and Moshe by dispatching venomous snakes that killed many among the people. In response to Benei Yisrael's repentance and pleas for help, God instructed Moshe to fashion a copper snake which would offer miraculous healing to anyone bitten by a snake who would look upon the image (21:4-9).
A famous Mishna in Masekhet Rosh Hashana discusses the nature of this "miraculous cure." The Mishna asks, "Does the snake kill, or does the snake bring life?" It responds that "when Israel would look upward and subjugate their hearts to their Father in heaven, they would be cured; otherwise, they would wither." The Mishna emphasizes that the copper snake did not possess any intrinsic, therapeutic power; it was rather a means of facilitating Benei Yisrael's sense of subjugation to the Almighty, in the merit of which they were cured from the bite.
Rav Chayim of Volozhin, in his Nefesh Ha-chayim (3:12), explains more precisely how the copper snake served this role. Twice the Torah emphasizes that the bite-sufferer would look at the copper snake, and not at the heavens (21:8-9). How, then, did this system ensure their subjugation to God? Rav Chayim explained that the spiritual process referred to by the Mishna required the patient to contemplate the snake, to focus his attention on the snake's natural capacity to inflict fatal injury. What God wanted was for them to ponder the natural risk posed by snakes, but then "subjugate their hearts to their Father in heaven," to understand that God's power exceeds and can overturn that of the snake. They were to reinforce their awareness of the fact that the Almighty alone determines one's fate, and that no natural force is free from His control. Once their faith in God's unlimited power was firmly established, they were cured from the fatal snakebite.
If, indeed, it was this awareness that was necessary for Benei Yisrael to be spared from the effects of the snakes, we might conclude that it was the absence or perhaps erosion of this belief that brought on the dire situation in the first place. The Torah records that Benei Yisrael requested permission from the Edomite kingdom to pass through its territory to reach Eretz Yisrael, but the Edomites refused, forcing Benei Yisrael to retreat and circumvent Edom. The people became exasperated and complained, "Why have you brought us from Egypt to die in the wilderness – for there is no bread and no water, and we are fed up with this miserable food" (21:5). In light of the Nefesh Ha-chayim's remarks, we might explain that the people longed to once and for all conduct a life governed by natural laws. They no longer wanted to live off heavenly manna, depending solely on divine grace; instead, they wanted soil to cultivate and rainwater to use to produce bread. But the desert experience was necessary to impress upon Benei Yisrael the awareness of God's indispensable role in sustaining them. The memory of their miraculous survival in the wilderness was to maintain their sense of dependence on His favor and grace even when they begin to self-sufficiently develop a country by tapping the natural resources of the Land of Israel. When the people expressed their desire for a natural mode of life, this reflected a desire to free themselves from their dependence on God and bear full responsibility for their sustenance. The Almighty therefore found it necessary to remind them of His unlimited power over the elements. To this end, He had them stare at and contemplate the image of the snake, and then remind themselves that God's power exceeds and can even reverse the powers of venomous snakes.