Explain who Mr. Dolphus Raymond is. What's his secret? Why do you suppose he shares his secret with the children?
Dolphus Raymond is a local "drunk"; or at least, that's what everyone thinks. He is a white man from a good family, but he has chosen to live on the black side of town with his mistress, who is also black. There, they raise their children, & live in relative peace. He is a source of rumor & speculation amongst the townspeople, because of his chosen lifestyle.
His secret? Mr. Raymond is not an alcoholic. In fact, all he carries in his brown paper sack is a bottle of Coca-cola. When Dill leaves the courtroom distressed, Mr. Raymond shares the soda with Dill, and talks with the children about tolerance and love. He explains that letting everyone think he's drunk helps them deal with the fact that he's chosen to ignore social standards, and instead pursue happiness with the woman he loves. He understands Dill's sickness at the cruelty he has witnessed during the trial, and explains that when they are grown, they'll no longer cry about the injustice in the world.
Mr. Raymond is another adult, like Miss Maudie and Atticus, who teaches the children a lesson in equality, and exteding compassion to all people. He shows that there are others in Maycomb who stand behind Atticus' decision to represent Tom, whether they can speak up in public or not. Mr. Raymond has chosen to keep a small secret in order to maintain his position in life, & he shares this with the children because he sees that they, unlike the other adults, will understand.
It says something about the level of racial prejudice in Maycomb that a white man has to pretend to be a drunk in order to live with an African-American woman. As far as the good folk of the town are concerned, drink is the only rational explanation for such eccentric behavior. As Dolphus says:
"[I]f I weave a little and drink out of this sack, folks can say Dolphus Raymond's in the clutches of whiskey—that's why he won't change his ways. He can't help himself, that's why he lives the way he does."
As Dolphus Raymond comes from a respectable family, his actions can't be explained away by the respectable townsfolk as typical "white trash" behavior. Dolphus is a Raymond, not a Ewell.
It also says something about the adults' intolerance that Dolphus only feels comfortable in revealing his secret to children. Their perspective on the world is altogether more innocent and less encumbered by the prevailing prejudices and social conventions of adults. The children, especially Scout, are aware of the huge chasm that separates the races in Maycomb, but they are too young to understand the bigger picture. Nevertheless, Scout does come to realize that people in Maycomb who don't fit in, for whatever reason, need to make some kind of compromise in order to live their lives.