Shire
A shire is an area in England that originally was under the control of an Earl, an earldom, e.g. Wiltshire, Yorkshire. They often cover all or part of a county. Both shires and counties were used as formal demarkations within the kingdom's administration, with their own reeves and sheriffs.
Strictly speaking, it is a tautology to say the County of Yorkshire, but it is occasionally done. Really it should be Yorkshire and the County of York.
Shires in the SCA
A shire is a local branch of the SCA which reports directly to a Kingdom or Principality. Shire is the next logical step up from Canton. The minimum requirement for a group to become a Shire is 5 sustaining-level financial members, and a petition that shows that the majority of the members of that group want the elevation.
A Shire has some minimum population and officer requirements, but less than that of a Barony. A Shire does not have landed nobility and cannot give out awards.
Once a group has become a Shire, their next elevation would be to Province or Barony.