A county borough was a type of local government district in England until abolished in 1974.
For example: rural districts may not be able to maintain footpaths or street lighting because of their size. Urban districts were based in a town and were able handle these jobs. Schools were the responsibility of county councils because districts were too small to run all types of schools themselves.
A county borough was a town big enough to run all its own local government, so the local county council had no power inside the county borough.