Before the local government boundary reorganisation of (I think) 1974, the county of Yorkshire was divided into three Ridings: North, West and East.
This is from Chambers online dictionary:
riding (noun) often Riding when part of a name) 1 any of the three former administrative divisions of Yorkshire, East Riding, North Riding and West Riding.
ETYMOLOGY: Anglo-Saxon as thriding, from Norse thrithjungr: third part.
Most people who live there/come from there still talk in these terms.
So it was/is a separate administrative area but is only one third part of the full county.