They didnt want to lose control of the people. The church was one of the main forms of government at the time. They didn't want the people to leave the faith and learn more about Gallilaos work.
Galileo figured out that the earth revolved around the sun (or he built on that theory). The Catholic church however, taught that the earth was the center of the universe. IF they were proved wrong (and they were) people would question their other doctrines and teachings, and so they wanted Galileo to keep quiet about his discoveries.
