Mr. Raymond offers Dill his paper bag. Scout think it's whisky, but nah, says Dill, it's just Coca-Cola.
This is Mr. Raymond's secret: he just pretends to drink all the time because it gives other people an excuse for his bad behavior.
He's telling them his secret because they're kids and they know better than their elders—Dill's crying shows that the world hasn't gotten hold of him and made him blind to its meanness.
Atticus sees it, too. He's an unusual case. All you have to do is look back inside the courthouse to see how unusual.
They head back to the balcony, to find Atticus already halfway through his closing remarks.
Atticus, after asking permission from the judge, takes off his coat, unbuttons his vest and collar, and loosens his tie—shocking his children, who have never, ever before seen him so undressed outside of his bedroom.
Atticus's tone sheds a few layers, too, becoming conversational rather than businesslike.
Basically, he points out that there's no evidence and that the prosecution is banking on the stereotype that all African-Americans are immoral liars who rape white women whenever they get the chance. He tells the jury that they're smart enough to see that for the lie it is, and to know that African-Americans are no worse than any other race.
At this point Scout notices another first: Atticus is sweating.
Atticus continues to the jury: he cites Thomas Jefferson's famous line that all men are created equal, and says that this doesn't mean that everyone is just as talented as everyone else, but that everyone is equal under the law.
He ends his speech with a plea to the jury: "In the name of God, do your duty" (20.52).
Atticus turns to go back to his seat, softly saying something else that Scout doesn't hear; she asks Jem, and he says that Atticus said "In the name of God, believe him" (20.54).
Calpurnia is making a beeline up the center aisle of the courtroom towards Atticus.