What persuades the lynching-party to give up on their attempt on Tom's life in To Kill a Mockingbird?
In chapter 15 of Harper Lee's To Kill a Mockingbird we find the Finch children, Jem and Scout, facing a lynch mob whose purpose is to attack Tom Robinson and, perhaps even, their own father, Atticus Finch.
Ever since the moment that Atticus Finch takes over the defense of Tom Robinson in court for his supposed rape of a white woman, the lives of both Jem and Scout change considerably. One of the most salient features of their new lives is that they have become more courageous than they have ever been; after all, the entire town of Maycomb is against Atticus for defending a black man regardless of the fact that Tom Robinson is, quite obviously, innocent of all charges.
All this is important to understand what happens next: After Atticus and his kids go to the jail to ensure the safety of Tom Robinson, the mob shows up to lynch Tom. Scout and Jem actively confront the mob. As a result, the mob threatens Jem, who is Atticus's only son, and give Atticus an ultimatum to get out. Scout, however, comes forward and makes the clever move that dissuades the mob from acting.
Scout sees that, among the mob members, is none other than little Walter Cunningham's father, Mr. Cunningham. Scout has had run-ins with the young Cunningham. In the beginning of the novel we find her attempting to explain the extreme poverty of the Cunninghams to her teacher. Later in the story we witness when she is made to eat lunch with the very hungry Cunningham boy and is told by Calpurnia that it is Scout's duty to treat little Walter Cunningham, and anyone who shares a plate with her at her table, as a welcomed guest.
It is imaginable that all these memories with the junior Cunningham shock and confuse Scout: Therefore, she wonders how can a family man in dire straits spend his energy trying to kill a man who should be presumed innocent. The father of the same boy whom she has been taught to treat with uttermost respect! This is the moment when she calls out Mr. Cunningham by name and last name, and reminds him who he is and the worthlessness of what he is about to do.
Facing Mr. Cunningham is the equivalent of taking away one source of energy from the lynch mob. Calling and singling him out is a way to point out that he has no business following a this group: He is his own person, and he does not have to play by the ignorant rules of Maycomb. This action immediately breaks down the gist of the mob and separates Cunningham from the rest of the men. And, like the saying goes: Divide, and conquer.
This exact question has already been asked and answered here on eNotes. Here are a couple of links for you: http://www.enotes.com/to-kill-a-mockingbird/q-and-a/what-persuades-lynching-party-give-up-their-55391 and http://www.enotes.com/to-kill-a-mockingbird/q-and-a/what-persudes-trhe-lynching-party-give-up-their-144029