A county is an administrative or ceremonial region with clearly defined geographical boundaries.
The formation of English counties can be traced back to the Norman Conquest.
A County or Cont`e was an area that was overseen by a Count.
Counties replaced the Saxon Shires. An old name for Shire is a Sheriffdom. Looked after by an official called a Shire-Reeve later known as a Sherriff.
Some counties in England have never been Shires. This is because they were either Kingdoms in their own right, (Sussex, Essex, Kent) or because they resisted Saxon invasion following the withdrawal of the Roman legions in 400 AD, (Cornwall, Devon and the whole of Wales).