Boo Radley does not change as much as the reader's perception of him. Whereas he's made out to be a night stalker and peeping Tom thriving off raw squirrels, he is just a very withdrawn man living in virtual (except for his parents) isolation. Boo seizes the first chance given to make contact with the Finch children and show himself to be on friendly terms. At the end of the story he displays courage in defending Scout and Jem from Mr Ewell. After this incident, though, he sinks back into his usual profile as a hermit avoiding celebrity, a kind man misjudged and shunned by society.
Scout learns compassion, not just in respecting Walter Cunningham but with people in general. After the schoolhouse incident, Atticus teaches her to step into other people's shoes before making a judgement call even if there is injustice. Atticus also teaches her the necessity to hear both sides of a story, as after the fight with her cousin Francis. Scout also learns that people can be basically good and just the same blighted by a vice (such as prejudice), much as the rabid dog rambling throughout the neighbourhood.
Jem has growing pains in his own coming of age as he realizes that injustice sometimes prevails despite people's effort to be fair. Sometimes the individual 'in the right' cannot "win" against a corrupt society, but it is important to stand one's ground just the same. As Scout, Jem also learns that people (such as Mrs Dubose) should not be judged by first impressions.
In the beginning, Boo is a source of fascination for Scout and Jem. He is the mysterious man on the street, kind of like living in the local haunted house. Due to the mystery of his lifestyle and the stories about his past, they do what they can to spy on him and learn more about him.
After Atticus scolds them, they stop pursuing their interests in Boo. He, however, has begun to notice them, and he leaves gifts for them in the tree. When Nathan Radley seals up the hole with cement, Jem understands that Boo's brother has cruelly cut off Boo's contact with the outside world.
As the trial starts, the fascination with Boo lessens. Then, of course, at the end, he saves the children from Bob Ewell's attack. When Scout stands on the Radley porch, she sees what Boo saw; images of herself and of Jem passing through life, in front of Boo's house, every day. They became the highlights of his day, and he began to think of them as his children. When they were in trouble, he braved the outside world to save them.
At the end of hte novel, the kids have learned to appreciate Boo, and to understand more of what his life must be like.