In chapter 13, Aunt Alexandra Finch comes to live with Atticus and the children for a while. Suddenly, the children find they must behave in a way that is becoming of the Finch family name. Scout reflects that to her, the label "Fine Folks" just meant that they were people who did their best and used common sense in their affairs. But Aunt Alexandra's concept of Fine Folks was different. To her, people were considered Fine Folks if they had occupied a family homestead for numerous generations. The idea is that the "older" families of a community are more worthy, more upstanding, and of better moral character than those who have recently moved in. Jem is wise enough to scoff at the concept, noting that the Ewells had been drawing welfare while living behind the dump in Maycomb for three generations.
The Finches, of course, were one of the founding families of the region. Their ancestor Simon Finch settled on Finch's Landing and became rich, and his descendants continued to grow cotton there. But Aunt Alexandra, who would certainly include the Finch family among Fine Folks, was "one of the last of her kind." The way Scout describes her would further define Alexandra's expectations for Fine Folks. Alexandra had "boarding school manners," she would embrace any moral that would come along, and she wanted the children to "behave like the little lady and gentleman that you are."
A term synonymous with Fine Folk might be "gentle breeding." Alexandra evidently coerced Atticus to have a talk with the children to encourage them to live up to the Finch name.
Your aunt has asked me to try and impress upon you and Jean Louise that you are not from run-of-the-mill people, that you are the product of several generations' gentle breeding ... so you might be moved to behave accordingly.
To sum up, Fine Folk come from established families in a region, follow strict standards for moral behavior, and display good manners in public.
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"The Levy family met all criteria for being Fine Folks" What these criteria are is answered in the following paragraph, they 'did the best they could' and had been living in Maycomb for 'five generations.'
There are a number of interesting points about the definition which Lee uses here. The use of capitals 'Fine Folks' may remind you of the way that Aunt Alexandra speaks, often representing traditional views within the community. Lee often asks us to examine these ideas.
Lee creates links within the novel. The Levy family are Jewish and here we see that racism against them is rejected. This can be connected to chapter 26 when the school teacher is telling the students about Hitler's treatment of the Jews however she is blind to her own inherent racism of the black community.
'Fine Folks' therefore is a term which should be used for people in the white and black communities equally - but usually isn't in Maycomb.