Burton is a village in Geauga County, Ohio, United States. The population was 1,407 at the 2020 census. It is part of the Cleveland metropolitan area. Burton is the location of Century Village, run by the Geauga Historical Society. The museum village is composed of 19th-century buildings moved there from other locations. Many special events are …Burton is a village in Geauga County, Ohio, United States. The population was 1,407 at the 2020 census. It is part of the Cleveland metropolitan area. Burton is the location of Century Village, run by the Geauga Historical Society. The museum village is composed of 19th-century buildings moved there from other locations. Many special events are held there each year, as well as at the Geauga County Fairgrounds, also in Burton.