When Scout and Dill returned from their break outside with Dolphus Raymond, Atticus had already begun his summation to the jury. It was then that she saw something she had never seen her father do
... before or since, in public or in private:
In an attempt to show that he was a common man to the jury, he first placed his watch and chain on his table. Then,
... he unbuttoned his vest, unbuttoned his collar, loosened his tie, and took off his coat.
This was unusual for Atticus, since "he never loosened a scrap of his clothing" until bedtime. To Jem and Scout, it "was the equivalent of him standing before us stark naked." Later, Jem and Scout witnessed another "first" when he wiped his glasses with a handkerchief. Atticus was a man who "never perspired," but he was sweating now.
As was mentioned in the previous post, the children are astonished to see Atticus unhitch his watch and chain before making his closing arguments. Atticus then unbuttons his vest and collar, loosens his tie, and takes off his coat. Scout mentions that she had never witnessed Atticus "undress" in public or private. The children are shocked at Atticus' actions, which seem equivalent to him standing naked in the courtroom from their perspective. Atticus loosening his formal clothes is his way of appealing to the blue-collar jury members. He wants to show the jury members that he is also a common man, who is in touch with the community of Maycomb. However, Jem and Scout misinterpret Atticus' actions and humorously believe their father is undressing in front of the jury.