Boo is used as a symbol of innocence and purity in Chapter 31. Scout mentions his extreme "whiteness," a color that is symbolic of both purity and innocence. He also represents the children's guardian angel, and when Boo touches Jem's hair, it is as if he is transferring his power of good--of healing--to Jem, a sure sign that he will survive his injuries. In addition to fulfilling Scout's long unfilled fantasy--of actually meeting and speaking with Boo--he helps to make the evening one in which she is able to enjoy a feminine, "ladylike" moment: that of being accompanied by a gentleman as they walk down the street.
... if Miss Stephanie Crawford was watching from her upstairs window, she would see Arthur Radley escorting me down the sidewalk, as any gentleman would.
The street lights symbolize a kind of enlightenment for Scout who, under their "fuzzy" glare, glimpses a new and unique view of her neighborhood. She stands on the Radley porch as if she were standing in Boo's skin--"in his shoes"--seeing the events of the past two years as if she were reliving them from his own eyes.
One of the characters from Jem's book, The Grey Ghost, from which Atticus is reading, features a character named "Stoner's Boy." Stoner's Boy serves to symbolize Boo, a character who was accused of many things but was proved to be innocent, and in the end,
"... when they finally saw him, why he hadn't done any of those things... Atticus, he was real nice."
"Most people are, Scout, when you finally see them."