The sch.uk second level domain is used for schools, where the definition of a school is given by the appropriate government agency.  Because many schools share similar if not identical names, geographical areas are used as third level domains to differentiate between the schools, so a registration would look something like

schoolname.area.sch.uk

Application procedures for .sch.uk Domain Names in England, Northern Ireland, Scotland and Wales are all slightly different as are the rules on what can be used a school name and an area name.  Full details are in the Schools section of the web site.