This incident occurs in chapter 8, when Miss Maudie's house catches fire. Scout does not realize that there is a blanket on her shoulders. It is cold outside, but she did not notice when it was put there. They realize it was probably Boo Radley that put it there, which is a frightening prospect for Scout.
This event is one of the first indications that Boo Radley is more than just the neighborhood legend. He is a real person, and actually not that frightening. Although Scout is still afraid of him, the consideration by the Finch family that Boo could do something caring and kind is a new development in our understanding of Boo, and represents the coming of age of the children. Jem especially sees him as a human being and maybe misunderstood.
When Miss. Maudie's house catches on fire, the whole town comes out to help. Atticus tells Jem and Scout to stand in one spot and not to move. It is a freezing cold night and the children are frightened by what has happened. That winter is the coldest winter people can remember. They have actually had snow, which is pretty rare in that part of the country.
Jem and Scout are so mesmerized by what is going on, that they don't even notice that someone has put a blanket around Scout's shoulders. Atticus gets mad at them, because he thinks they disobeyed him and went back to the house to get a blanket. Jem and Scout promise they hadn't been anywhere and Scout can't explain how the blanket got around her. Jem realizes that Boo was the one who had put the blanket around Scout. This makes Jem realize that Boo was watching them, and showing concern for Scout, he had slipped out and placed a blanket around her. This makes Jem realize that Boo is not the scary person they all believed him to be.
In this chapter, we see more of the love that Boo has for Jem and Scout. He wants them to be safe. He was concerned for Scout. He is showing a real protectiveness over the children. We see that Jem is starting to realize that Boo is actually a good person and not someone to frightened of anymore.