How does Harper Lee show change/maturation of Boo Radley's character in To Kill a Mockingbird?
Although Radley doesn't appear until the end of the novel, he makes brief "appearances" throughout the book as it becomes apparent he is watching the children from the prison that is his home. At first, he leaves them little gifts in the crook of the tree; once, Scout even hears him laughing from inside when she crashes into the curb inside a rolling tire. He sews Jem's pants back up and leaves them on the fence for Jem to retrieve on the evening the kids are trespassing on his parents' porch, and places a blanket on Scout's shoulders the night she is standing in the cold when Miss Maudie's home burns down. Finally, of course, Radley saves the children's lives when Bob Ewell attacks them in the dark on Halloween.
The fact that Radley was coming out of his house at all over this period of time was unusual; the fact that he saved the children, and carried Jem home, allowing himself to be seen by Atticus, Scout, Alexandra, and Heck Tate was monumental, given the years of his confinement. Although Scout mentions that she never saw him again (so this wasn't the beginning of a whole new life for him), the changes in him, however small, permitted him to venture forth to save the kids at a critical moment, clearly a sign of some personal growth.