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]
Any given county even in the same state could have less than 2,000 people to more than 10,000,000 people and could have an area from less than 1,000 square miles to more than 20,000. It's also not relevant from a constitutional standpoint. If you look at the nation as a whole you have even larger extremes with counties as small as 88 people or just 12 square miles. Looking at population density nationwide you have extremes from 69,000 per square mile to 0.03 per square mile.
IMO the people who talk about how many counties they won are looking for any sort of stat they can use to try to claim a "win". Would be no different than if people talked about how many area codes their party won (though I suspect area codes would be at least a little bit more consistent from a population distribution standpoint).
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...
The campaign would not have looked like this: http://thehill.com/homenews/campaign/294716-will-trump-or-clinton-win-the-11-states-deciding-the-race
In any case my support for such a system isn't even related to the results of the 2016 election, I've been saying the same thing for decades.
Will Trump or Clinton win? The 11 states deciding the race
The final sprint toward Election Day has begun.