There are two wiki articles that actually happen to be good starting points and then another excellent source of information about the formation and functions of counties in the US are genealogic books that cover state and county functions in regards to records keeping that actually subdivides the types of counties and how and why they were formed the way that they are.
https://en.wikipedia.org/wiki/County_(United_States)
https://en.wikipedia.org/wiki/Political_divisions_of_the_United_States
http://www.ancestry.com/wiki/index.php?title=Red_Book:_American_State,_County,_and_Town_Sources
There are other resources available, but these three are a good start.
County (United States) - Wikipedia
In the United States, an administrative or political subdivision of a state is a county, which is a region having specific boundaries and usually some level of governmental authority.[1] The term "county" is used in 48 U.S. states, while Louisiana and Alaska have functionally equivalent subdivisions called parishes and boroughs respectively.[1]
See: https://www.dailykos.com/stories/2017/1/30/1627319/-Daily-Kos-Elections-presents-the-2016-presidential-election-results-by-congressional-district
Daily Kos Elections presents the 2016 presidential election results by congressional district
Daily Kos Elections has been working to calculate the 2016 presidential election results by congressional district, and thanks in large part to the tireless efforts of Jeff Singer, we finally have the numbers for all 435 congressional districts. You...