From Michael Robinson’s blog, TimeToEatTheDogs.com:
[Frederick Jackson Turner] linked the frontier to the story of American progress, arguing that it rejuvenated American culture by placing pioneers into contact with the wild, savage world at the edges of civilization. In the process, pioneers had to break from the strictures of the civilization they left behind and re-imagine life from the ground up. In the process, Turner argued, they recapitulated the long arc of human society from savagery to civilization, infusing American society with the energy of their innovations.
The frontier thesis was (and in some quarters, still is) seen as a compelling story of American uniqueness. In it, supporters found a story to justify a view of Americans as a special, exceptional people.