When the first county councils were created, it was decided that to let them have authority over the large towns in them would be impractical, and so any large incorporated place would have the right to be a county borough, and thus politically independent from the administrative county it would otherwise come under. Initially, a town had to have a population of over 50,000 to apply for county borough status, but this threshold was raised to 75,000 in 1926, and 100,000 later on.
This situation did not persist and many of the old county boroughs that were annexed, have now regained independence as unitary authorities - essentially the same as county boroughs, but renamed. In Wales some of the unitary authorities are called county boroughs.
All of the former county boroughs in Wales are now unitary authorities.
In the Republic of Ireland, the relevant legislation remained still in force (although amended), and county boroughs on the original model existed prior to 2001. Under the Local Government Act 2001 (which replaced most existing local government legislation in Ireland), the term "County Borough" was abolished and replaced with "City" (and hence, "Corporation" with "City Council"). However Kilkenny, while a city, is instead regarded as a town (and part of the county council area) for local government purposes. It is allowed to use the title "Borough Council" instead of "Town Council" however.
In Scotland, they were not called "county boroughs" but instead "counties of cities". These were abolished in on May 16, 1975. All four Scottish cities of the time were included in this category - Aberdeen, Dundee, Edinburgh, and Glasgow. There was an additional category of "large burgh" in the Scottish system, these covered everything apart from police, education and fire.
For all practical purposes, county boroughs are exactly the same as the other principal areas of Wales called `counties' or `cities' as all these areas are run by unitary authorities (i.e.: have the functions of both boroughs and counties).
Historical county boroughs
This table shows those county boroughs that existed in England and Wales between the Local Government Acts of 1888 (that created them) and 1974 (that abolished them). It also shows which of those places has become a unitary authority again since, either as-is or as part of a larger unitary authority.