In chapter 15, Jem, Scout and Dill sneak over to the jail to see what Atticus is up to. When a lynch mob shows up and starts talking to him, Scout hears her father say something that catches her attention: "Do you really think so?" (152). She thinks that "somebody's man would get jumped," so she runs across the square, through the crowd of stinky men, and up to her father to check things out. She says that she thought Atticus would find it a fun surprise to see her there, "but his face killed my joy."
Scout happens upon this serious situation with a child's heart. She knows that something intense might happen, but she doesn't understand the gravity of the situation that she charges into. Her childlike sense and innocence guides her to take an awkward situation and use it as an opportunity to practice what her Aunt Alexandra has been teaching her to do—be a lady and talk politely. That's exactly what she does as she singles out her classmate's father, Walter Cunningham. She reminds him that he brought her family hickory nuts and that she's friends with his son. She talks about a boy he loves and reminds him of the innocence and sweetness in life.
Finally, after Scout yammers on for a little bit longer about Cunningham's legal entailments, things get more awkward. It isn't until Mr. Cunningham's guard is finally dropped that he says, "I'll tell him you said hey, little lady. . . Let's clear out. . . Let's get going, boys" (154). Atticus later says:
". . . it took an eight-year-old child to bring 'em to their senses, didn't it? . . . That proves something that a gang of wild animals can be stopped, simply because they're still human" (157).
Scout diffuses the situation by talking.
More specifically, she talks directly to Mr. Cunningham, who she recognizes. By talking about his legal business and his son Walter, who is in her grade, and by being polite in general, she brings him back to their shared humanity.
She talks about what Mr. Cunningham (one of the rioters) is interested in, his son Walter. She talks about how he's a nice guy and how he went to dinner with them once. She reminds him that he's just like Atticus. She reminds him that he has a child at home, just like Atticus has two. They all need to be taken care of. She reminded him that he was human and since he was most in charge, he told everyone to leave.