Interestingly, American English accents come from exactly where you might think they come from.
American English at its foundation is closer to how English people spoke in the 1600s. The most identifiable pronunciation feature is rhoticity -- the hard "R" sound in words like "hard," which was common in English on both sides of the Atlantic 400 years ago, which was largely abandoned in the UK over the centuries but not in the US.
UK and US English are different in many other ways, as well.
Also, American English tends to be unusual in the use of flat vowels, short "a" sounds and the use of the "Rhythm Rule," which is the tendency of American English speakers to alternate between stressed and unstressed syllables.
Beyond that, most regional American accents can be explained by the movement of people from outside the United States, and movement within.