In the book To Kill a Mockingbird, how does the character of Boo Radley contribute to Scout's coming of age?

I think you are asking how Boo Radley's character contributes to Scout's coming of age in To Kill a Mockingbird. The novel, which Scout narrates, begins when she is almost six years old and ends when she is almost nine; thus she naturally matures as the story unfolds. In addition to the age factor, Scout's maturity is impacted by the events she witnesses in Maycomb, including Tom Robinson's trial, the behavior of the lynch mob at the jail, and all of the children's dealings with Boo Radley.
Although she is frightened by Boo (and by the mere idea of him) at the beginning of the story, Scout becomes more accepting of him after receiving the gifts he leaves in the tree, which leads to a sort of friendship between Boo and the Finch children. Boo ultimately saves Scout and Jem from Bob Ewell's attack later in the novel, putting their theoretical friendship into action. The deepening relationship between Scout and Boo contributes to her maturity by encouraging her to cultivate empathy, compassion, and courage in an unjust world.