The Regions of countries screen is used to (optionally) maintain a list of regions in a country, and how those regions are presented on screen.
If a list of regions is created for a country then only those regions can be entered in the corresponding address for contributors in that country.
Regions can be displayed differently by country. By default a region is a County, but this can be changed to whatever is appropriate e.g. State, Province, or Territory. The postcode fields can also be re-labelled as required for contributors from any country. For example it is more normal to refer to zip codes in the USA.
A requirement of the USA's Form 1099 tax reporting is that a valid State must be provided for all reportable contributors. Consequently all Form 1099 countries (as flagged by the Form 1099? checkbox), have a list of States associated with them. The same is done for territories and provinces of other countries to help improve the quality of the data.