In Parshat Chukat we read about the story of Hashem sending the snakes to bite the people as punishment for (yet again) complaining how Moshe could dare take them out of Egypt with no bread or water in the desert. Hashem sends the poisonous snakes to bite them and people start dying.
In 21:8 hashem tells Moshe to make a “saraf” (fiery serpent) and place it on a pole. Whoever would look at it would be healed and whoever would not look at it would not be healed. Rashi brings the words of Chaza”l who ask how could looking at the snake heal the people? Rather when they would look at the snake they would remember their Father in Heaven, Hashem, and repent. Those who did not look at the snake would have no catalyst to cause them to think about Hashem and repentance, hence they would die.
Why did this have to be part of the healing process? Moshe davened to Hashem to stop the snakes and Hashems response was to put a snake on a pole. Why did He require this? He has sent many plagues in the past which he cancelled without doing anything so strange, so why here did He require such an act of participation on the people’s behalf?
Because their sin was one of lack of faith (they asked and complained about having been taken from Egypt into a barren desert), Hashem could not just heal them and let bygones be bygones. Next week it would happen again, as it has already occurred a number of times. The only way to nip it in the bud was to make them realize on their own what their mistake was. By telling Moshe to put the snake on a stick and make them look at it to get healed, He was forcing them to think about what they had done wrong, thereby allowing them to repent for the lack of faith. Living in the desert was an experience of truly miraculous proportions. Every moment they were surrounded by unusual miracles. They just did not think about them and realize Hashem is taking care of them.
Their participation in the healing process would force them to think about it and later to remember the lessons of the past, thereby ensuring it would not happen again.
When you participate in a process, the results are often internalized in a much greater way than by one who simply observes from the outside.