What major role does Scout play to calm Mr. Cunningham and help Atticus?

In Chapter 15, Atticus stations himself outside the jailhouse to guard Tom Robinson, his client accused of and about to stand trial for rape. While outside the jailhouse, a group of men confronts Atticus and tries to persuade him to let them by, ostensibly so they can cause the prisoner (Tom Robinson) physical harm. Unbeknownst to them all, Atticus' two children and their friend Dill are spying on them nearby, and Atticus' daughter, Scout, bursts onto the scene. Scout informs the reader that "I sought once more for a familiar face, and at the center of the semi-circle I found one. 'Hey, Mr. Cunningham" (Lee 175). 
By singling out an individual from the mob formed outside the jailhouse, Scout accomplishes several things. First, she reminds them that they are known individuals in the town, and in this way reminds them they are accountable for their actions as individuals. She also mentions Mr. Cunningham's son, which, coupled with her own childishness, serves to remind the crowd that they are threatening a fellow father and family-man (Atticus). Finally, before Scout intervened, the mob viewed Atticus as an enemy and obstacle to the goal of maiming Tom Robinson. Once Scout appears, they once again view him primarily as Atticus Finch, father of two, and fellow neighbor: a man they consider one of their own. 
These revelations disquiet the mob, and make them question their intended actions. In short, Scout inadvertently shames the men. She makes them feel poorly and shy away from their original decision to commit violence, both by reminding them of Atticus' role in their own lives, and inserting her childhood innocence into what was about to be a dark, violent scene. It is enough to derail their plans, and lead by Cunningham's polite response to Scout's chatter, they do not move forward with their attack. As Atticus later puts it, "you children last night made Walter Cunningham stand in my shoes for a minute. That was enough" (Lee 180).

In chapter 15, the Old Sarum bunch surrounds Atticus outside of the Maycomb jailhouse in an attempt to lynch Tom Robinson. While the men are circled around Atticus, Jem and Scout (accompanied by Dill) are secretly watching their father speak to the mob from across the street. However, Scout cannot contain her curiosity and runs out into the middle of the group, which surprises Atticus and the Old Sarum bunch. When Scout enters the group of men, she recognizes Mr. Cunningham and attempts to strike up a conversation. Scout mentions that she goes to school with Walter Jr. and brings up Mr. Cunningham's legal entailments. Despite his numerous attempts to ignore Scout, Mr. Cunningham begins to view the precarious situation from Atticus's perspective and finally acknowledges Scout. Shortly after speaking to Scout, Mr. Cunningham tells the Old Sarum bunch to leave the scene. Scout's presence made Mr. Cunningham aware of his actions and allowed him to sympathize with Atticus, who was in a difficult position.