Atticus, a very polite, formal man who was a stickler for manners, was never seen without tidy clothing; he was always buttoned, his tie was up tight, and no one had ever seen him any differently, including his children.  But in the courtroom, as Atticus is about to give his closing testimony, he does something unusual.  He "unbuttoned his vest, unbuttoned his collar, loosened his tie, and took off his coat." Scout says of this that that she "never saw him do [that] before or since, in public or private...he never loosened a scrap of his clothing until he undressed at bedtime."  This just emphasizes how important Atticus felt his closing testimony was; he wanted to appear like the other men.  He wanted to seem approachable, honest, vulnerable and sincere, and loosening his tie was a way to say to the jury, "Look here.  I'm going to be honest with you for a bit.  Let's have a chat, just you and me."  It made him seem more down-to-earth, and one of the gang.  It is an interesting strategy, or maybe just a natural instinct that went in line with Atticus' sincerity in the moment.  But, according to Scout, it was highly unusual.