In a short story, the setting is a crucial element and, as it creates mood and circumstance, it can be as important as the theme. Short stories need to convey their message in a very short space of time and so, without a ready and easily recognizable setting, a reader can get lost and fail to understand the story. A novel has many chapters and builds characters, all of which contribute to the setting, whereas, in a short story, this is not possible. Characters can only develop quickly if the setting is apt and clear. Setting includes time and place but also, possibly, historical references, geography and even the culture in which the story exists.
Thank You, M'am by Langston Hughes makes good use of setting, even making the reader aware of Mrs Jones' own financial circumstances and that she is not a wealthy woman herself; even her language use reveals something about her as do her living quarters (culture), but she still gives $10 to Roger. The story begins late at night as Mrs Jones walks home from work (time and place) and the reader can immediately relate to a purse-snatching taking place (culture). There is a historical aspect as the reader learns that Mrs Jones has "done things too." The geographical aspect of setting is not mentioned but teh descriptive elements in the story allow the reader to assume that this takes place in a working class part of town, perhaps inner city.
Dubliners by James Joyce is a series of short stories with a strong geographical setting - Dublin, Ireland - and a historical setting of the late nineteenth century. The cultural element is unmistakable as, and to use Eveline as an example, Eveline, a dutiful daughter, must make the choice between duty and a desire to "escape" the life she is otherwise doomed to. Eveline is trapped in her life and sits in her father's house (time and place) contemplating her future and whether, actually, it really is "a wholly undesirable life" after all. She does not have much time left to make a decision and, ultimately watches "like a helpless animal" as the ship to Buenos Aires, and her future disappear.
The above examples are just a few of the many short stories to choose from which illustrate setting well.