Characters who change in a significant way over the course of a story are called “dynamic” characters. Just like people in real life, characters don’t change easily. It usually takes some sort of difficult experience or event to change us.
Scout and Jem’s character change is evident at the end of the story. On page 279 of the Warner Books paperback, Scout says to the reader,
Atticus was right. One time he said you never really know a man until you stand in his shoes and walk around in them.
Here, the author is repeating a phrase that Atticus said earlier in the story. At that time, Scout did not understand what he meant. Now as a result of her experience, she does. This is an important change.
Finally, in the last several paragraphs, Scout speaks to Atticus about Boo Radley, saying with a kind of soft surprise, “Atticus, he was real nice.”
For Scout to say this about Boo signals a momentous change. She and Jem have spent the entire book in terror of Boo, imagining all sorts of horrible things about him.
Writers often show character change in just this way. Establish an idea, let it run through the story, then show how the characters' attitudes toward this idea change.