What does this quote mean?
"I never understood her preoccupation with heredity. Somewhere, I had received the impression that Fine Folks were people who did the best they could with the sense they had, but Aunt Alexandra was of the opinion, obliquely expressed, that the longer a family had been squatting on one patch of land the finer it was."
Aunt Alexandra does not approve of Atticus' parenting skills primarily because he teaches his children to treat each individual as they deserve to be treated, regardless of social class.. Moreover, this particular quote will have a more powerful impact upon those who read the book after the glorious speech made by Dr. Martin Luther King Jr. Recognized as the I Have a Dream speech Dr. King suggests that it is the content of ones' character...not the color of their skin that determines the worth on an individual. That is what Harper Lee meant when she wrote those words that came out of Aunt Alexandra's mouth...Her words were fiction, yet their meaning was fact.
What this quote is expressing is the difference between Atticus's ideas (as passed down to his kids) and Aunt Alexandra's ideas as to what kind of people were high class.
To Aunt Alexandra, it was bloodlines that made people high class. If your family had deep roots in the area (had been on one patch of land a long time) then they were something.
But to Atticus, quality depends on what you do with your life, not who you are. It depends on "doing the best with the sense you have."
So what you have reflected in this quote is a very snobby attitude against a more democratic attitude.
Aunt Alexandra retains a certain attitude of the importance of what one is as a determinant of who one becomes.
In the exposition, Scout mentions that some members of her family find it shameful that they cannot trace their ancestral line back to "either side of the Battle of Hastings." This was the battle of William the Conqueror of Normandy, France, and the Anglo-Saxon Harold Godwinson—both men of royalty.
Alexandra takes pride in the Finches' family tree because good breeding is important to her. She is convinced that the qualities one inherits are very much the determinants of what one becomes. Thus this quote indicates a certain haughty tone. While Scout is rather naïve in her narration of her aunt's attitude, the effect of Scout's description is satiric. Through the innocent voice of Scout, Harper Lee mocks established and old-fashioned beliefs by depicting them in an absurd manner.