What is Scout's most important action in To Kill A Mockingbird?

Scout's most important action is her approaching and addressing Mr. Cunningham during the mob scene outside the jailhouse.

In Chapter 15 Scout hears her brother Jem in his bedroom. She knocks on his door, asking him what he is doing. "I'm goin' downtown for a while," he replies. Scout asks him why he is going at ten o'clock at night, but he is somewhat evasive. After their aunt's light goes out, the children sneak out and pick up Dill on the way. Jem tells Dill only that he just has "a feeling."

The children look first at Atticus's office, then in the bank. Finally, they decide to check Mr. Underwood's office which looks over the jail. They find Atticus sitting in front of the jail with a light over the door. Soon, the children witness a stream of dusty cars driving up. Men get out of these cars in pairs and surround Atticus, hiding him from the children's view. They speak in whispers: "He in there, Mr. Finch?" and "You know what we want."
But, Atticus only addresses Walter Cunningham, saying that they should depart, and that Heck Tate is around somewhere. But, another man contradicts Atticus, saying that Heck has been sent on a wild-goose chase.

When Scout hears her father say a familiar phrase used when he plays checkers and someone is about to make a bad move, she rushes forward, followed by Jem and Dill. Atticus shows fear when he sees the children, and a man tells Atticus to get the children out of there. When a burly man grabs Jem, Scout kicks him. As the tension rises, Scout looks at the men, then addresses one whom she recognizes,

"Hey, Mr. Cunningham. How's your entailment gettin' along?"

Mr. Cunningham is taken off guard by Scout's address. As he shifts his feet, Scout tells him who she is and that she goes to school with Walter, his son. Then, she continues talking about entailments, but becomes uncomfortable with so many people looking at her. Finally, the tension is broken as Mr. Cunningham kneels down and tells Scout that he will tell his son that she says "hello." Then, he orders the men to go: "Let's clear out....Let's get going."

After the mob leaves, Tom Robinson asks, "They gone?" [sic] Atticus assures him that they are. Soon, Mr. Underwood appears in his office window with a double-barreled shotgun in his arms. Clearly, Scout has diffused a very tense situation.