The best examples for your question probably come from the children in the novel. After Dill is found under Scout's bed after running away from home, he decides why Boo Radley never leaves his house and why he has never run away himself.
"Maybe he doesn't have anywhere to run off to..."
Jem also has his ideas about Boo. Upset with the verdict of the jury and with Aunt Alexandra's refusal to allow Walter Cunningham Jr. to visit the Finch house, Jem realizes that the people of Maycomb don't always act in a loving manner.
"If there's just one kind of folks, why can't they get along with each other? If they're all alike, why do they go out of their way to despise each other? ... I think I'm beginning to understand why Boo Radley's stayed shut up in the house all this time... it's because he wants to stay inside."
Scout recognizes the hypocritical nature of her teacher when she compares Miss Gates' words about Hitler and the Jews, and her conversation about Maycomb's black citizens.
"Jem, how can you hate Hitler so bad an' then turn around and be ugly about folks right at home--"
Scout, for instance, shows insight, etc., when she accompanies Boo down the steps of her own house to his, after Boo has saved her brother. She knows that "a lady" would be led by "a gentleman" and that Boo has certainly proven himself. Thus, she tucks his arm around hers and lets him "lead" her. She is showing insight, maturity, and understanding by demonstrating an awareness of her culture and of Boo's place in it, and then making sure she does what is best for Boo.