Why did people move to cities and away from manors during the middle ages?

Most didn't, or didn't have the opportunity. Cities were generally free of seigneurial burdens, and urban residence often released peasants of their obligations to their lord, sometimes after a year and a day, though newcomers might face a new range of obstacles, for instance in entering trade. "Stadtluft macht frei", ran a German saying: "City air makes you free".