One of the central lessons learned by Scout and Jem is the lesson of empathy. They also learn that justice is not automatically carried out, but that it depends on individuals to work for it and defend it. Even then, justice is not always done.
Both Jem and Scout come to realise that life is not always fair, that good does not always triumph over evil.
Scout and Jem both learn to "walk in someone else's shoes" before they judge. Scout learns this in relation to her experience at school. Atticus tells Scout that before she judges her teacher harshly, she should try to see things from Miss Caroline's point of view.
This lesson is extended to episodes including the lynch mob, the jury at Tom Robinson's trial, and (most notably) Boo Radley. As the two Finch children grow over the course of the novel, this lesson is central to their burgeoning maturity.
In the events surrounding the trial, Jem and Scout also realize a hard lesson about town they live in. Maycomb is not the ideal place they had believed it to be. The residents, demonstrating local prejudices in attitude and behavior, act in ways that surprise and disappoint the children.
As witnesses to the events surrounding Tom Robinson’s trial they see a miscarriage of justice, with an innocent man condemned before he even enters the courtroom.
Jem is especially let down by the town's behavior at the trail. He learns, however, that one must work to defend those who are powerless to defend themselves, even if that defense is bound to failure. Atticus both states this ethic directly and acts it out in his role as Tom Robinson's attorney.