In Chapter 20, Dolphus Raymond gives Dill a drink of Coca-Cola from his brown bag and discloses his secret to the children. Dolphus confides in Scout and Dill that he feigns alcoholism in order to avoid conflict with his neighbors for his taboo way of life. Dolphus openly associates with African Americans and even has several biracial children. In the prejudiced community of Maycomb, Dolphus' way of life is scorned. Dolphus refuses to change his lifestyle and feigns alcoholism so that people "can latch onto a reason." Dolphus then attempts to explain Maycomb's prejudice to the children and laments about how the majority of white citizens unfairly treat African Americans. Scout and Dill's conversation with Dolphus Raymond gives further insight into the prominent themes of prejudice, race relations, tolerance, and innocence. Dolphus tries to explain to Scout that her father is different from the prejudiced citizens of Maycomb, but she innocently struggles to comprehend his explanation. Dolphus also discusses how the racist citizens are intolerant to his way of life and comments on how African Americans are unfairly treated. Lee explores these issues in depth throughout the entire novel, and this conversation contributes thematic insights to the story. 

In terms of prejudice and tolerance, when Scout and Dill realize that Mr. Raymond isn't really the town drunk (drinking Coca Cola instead), they are shown a new insight into his character.  They realize that he is giving the white community the impression he is a drunk because then they will make life so difficult because he prefers to live with African Americans.  Indeed he has several bi-racial children.  He advises them to not cry over the trial but to cry over the evil people practice upon each other - regardless of race - each and every day.  Once we can conquer that evil, then we won't have to worry about racism and intolerance.

This little scene also ties into the role of innocence and experience.  There are several examples in the book where Scout has her innocent world view challenged, such as when she sees Atticus shoot the rabid dog, when she sees how Calphurnia acts differently at the black church, when she sees Miss Maudie's attitude after her house has burned down, when she feels sorry of Mayella Ewell during her testimony.  This is just another moment in their lives where they realize that the people are not always what they appear to be.

During the trial, Dill gets upset because the prosecution lawyer is treating Tom Robinson rudely and unfairly. For example, he calls him "boy" and seems not to take the trial seriously. Scout takes Dill outside because he is crying, and she wants him to have a chance to get hold of himself.

Outside of the courtroom, Dolphus Raymond offers Dill a drink from his bottle hidden in a paper bag. To Scout's shock, it contains coca-cola and not whiskey. This relates to two major themes of the novel: that children have the innocence to see clearly and that people are often not what they appear.

Dolphus explains to the children that he only pretends to be an alcoholic because it gives people a way to make sense of why he is living and having children with a black woman, a strong social taboo. When Scout asks Dolphus why he entrusts his secret to her and Dill, he says it is:

Because you’re children and you can understand it.

Dolphus knows that Dill is crying because Robinson is being mistreated for being black: Dill can see beyond the color of Robinson's skin to his worth as a human being. Dill can perceive this so clearly, because as a child:

Things haven’t caught up with that one’s instinct yet. Let him get a little older and he won’t get sick and cry. Maybe things’ll strike him as being—not quite right, say, but he won’t cry, not when he gets a few years on him.

Adults, Dolphus implies, become jaded and accept a corrupt social order.

Dolphus also illustrates the theme that runs through the book that people are often not what they seem on the outside. Scout has been taught that Dolphus is "evil," but she finds he is a good man, just as she finds Boo is not what he seems.

There are literally dozens of examples throughout the novel, but I assume you are speaking of Jem and Scout's encounters on the day of the trial. During this time they discover many new things. (The examples below cover the primary themes of the novel, including Loss of Innocence, Ignorance vs. Knowledge, Courage vs. Cowardice, Predjudice vs. Tolerance, Innocence vs. Guilt.)

Before the trial begins, the kids watch the crowds of citizens pour into town for the trial.

• They witness Dolphus Raymond "lurch by" on his horse. They assume--incorrectly--that he is drunk. (Tolerance)
• Jem comments that the Mennonites "can't shave after they marry" because their wives "like for 'em to tickle 'em with their beards." (Ignorance, Loss of Innocence)
• Scout learns from Jem the definition of a "mixed child" when they further discuss Mr. Raymond. (Loss of Innocence, Knowledge)
• Jem and Scout discover that Atticus was appointed to defend Tom Robinson, and that he did not volunteer. (Knowledge, Loss of Innocence)

When Dill's crying becomes uncontrollable, he and Scout take a break outside where they meet Mr. Raymond up close and personal.

• They discover that Mr. Raymond is friendly and generous. (Knowledge)
• They find that the drink in the paper bag is only Coca-Cola--not whiskey. (Knowledge, Loss of Innocence)
• They determine that Mr. Raymond prefers the company of Negroes. (Tolerance, Knowledge)
• Mr. Raymond reminds the children to just "step back inside the courthouse" to see the racial prejudice that fills the townspeople. (Prejudice, Tolerance)

After the jury breaks to decide a verdict, Jem and Scout take a break for supper

• Jem is certain of an acquittal. (Innocence)
• Calpurnia is angry that the children witnessed the rape trial. Miss Rachel has "run distracted lookin' for you." Aunt Alexandra "nearly fainted." (Tolerance)

Tom is found guilty.

• Jem is angry, and it is his "turn to cry." (Loss of Innocence)