The definition of the short-story cycle is something along the lines of “an interconnected collection of stories.” The definition is a bit vague and people can argue which works are considered a “short-story cycle,” but some of the ones that are usually agreed on are In Our Time, Dubliners, Go Down, Moses, and Winesburg, Ohio. I would include a few of my favorites: What We Talk About When We Talk About Love, Big Bad Love, and Airships.
While curious about the importance of the short-story cycle in American Literature – by curious I mean procrastinating and googling around – I came across this essay that I thought I’d share:
http://www.triquarterly.org/craft-essays/born-workshop-mfa-and-short-story-cycle