The setting of William Faulkner's "Barn Burning" is relevant to the story in a number of differeant ways. Thus, the setting in the south is relevant to the distinction between the aristocratic or upper-class characters (such as the major) and the lower-class characters (such as Snopes). The south was also an area of the country in which itinerant farmers such as Snopes were more common than in the north. Finally, the south was also a place in which racial prejudice was not uncommon, as Snopes's own comments make clear. The south was a more impoverished part of the country than the north, and so the economic resentment that Snopes feels and represents was not uncommon in the south.
The main influence of the setting is the post-Civil War South. That was a very interesting time for the country, and the South specifically. Sharecropping was very common then, and you can see how sharecroppers were treated.