In Chapter 21, Jem clearly believes that the verdict in Tom Robinson's trial will be one of innocence. At one point near the beginning of the chapter, Jem can hardly contain his excitement, ask, "We've won, haven't we?" A few paragraphs later, he asks his father, who is serving as Tom Robinson's attorney, "You think they'll acquit him that fast?" Jem has not yet realized the power of prejudice in his society and believes that the members of the jury will do what is right. Atticus, on the other hand, does not tell his son directly that he does not believe he will win the case, but does suggest that the jury will take little or no time to deliberate in reaching their verdict; he is also well aware of the views of those deciding Tom Robinson's fate and holds no false hope.
Jem is idealistic: his idea of justice is based on what should be, not the reality of the community in which they live. When he sees Atticus, he asks, "We've won, haven't we?" Reverent Sykes takes a more prudent point of view, saying “Now don’t you be so confident, Mr. Jem, I ain’t ever seen any jury decide in favor of a colored man over a white man.” He attempts to soften the blow before Jem's optimism is destroyed by the racism of the town.
Atticus knows the true nature of the men sitting on the jury. He tells Jem that the jury most likely won't be out long, & when Jem asks if that's because they'll acquit Tom quickly, "Atticus opened his mouth to answer, but shut it and left [them]." Atticus knows he will lose, but he also knows that he has done the right thing in defending Tom, & not only that, but he's done his best as well. He didn't just take the case & go through the motions; he fought as well as he could, using his moral strength to guide him. Even though he doesn't want to disappoint Jem, and ruin his idealism, he knows it's important for his children to truly understand. So he allows them to watch the verdict being read. Even though it may be painful (and indeed, Jem cries with anger), Atticus sees this moment as essential in his childrens' maturation.
When the reader comes to that part they realize the innocence held by children such as Jem. Jem knows his father is doing the right thing and believes that Tom will be considered innocent based on the facts his father presented. Yet Atticus understands that the innocent will be declared guilty because they are of the different race and the society based around them is so harsh.