People moved into cities during the industrial revolution because:

They wanted higher factory wages.

To get jobs in factories, down mines etc. The Agricultural Revolution had led to enclosures of land, which m eant that many people could no longer earn a living from the country. The small farms that used to support most people were replaced by large farms belonging to a smaller number of landowners. The small farmers were driven out to look for work elsewhere. Some of them became farm labourers, working for the big farmers instead of running their own small farms. Others went to the towns.

The industrial revolution brought about a massive change in the way people worked for everyone, not just the small farmers. Prior to the revolution, most people worked in or near their own homes. Crafts like spinning, weaving, pottery etc were carried out at home, not in factories. Whole families tended to be involved in whatever the family enterprise might be. The Industrial Revolution obliged people to go and work in factories instead of working at home. The home and the workplace had become irrevocably seperate. People no longer worked for themselves, but for other people.