The blanket that mysteriously appears around Scout's shoulders on the night of Miss Maudie's house fire was placed there (without Scout's knowledge) by Boo Radley. It served as the final bit of evidence that Boo was a kindly soul who wanted to be the children's friend. It fueled Scout's fantasy of one day meeting Boo and engaging him in small talk.
The blanket is a significant gesture on Boo Rafley's part. It shows gentleness, compassion, and courage. Boo is becoming increasingly involved in the children's lives, watching them and looking out for them. The reactions of Jem and Atticus are also significant. So is Scout's. She doesn't understand the conversation at that time, but at the end of the book she does. She's growing up.
The blanket is significant because it shows Boo's true nature and kind attitude toward the children. This is the first direct contact he has had with Scout. This gesture proves that he is not the vicious man he has been portrayed as. The reactions of Scout and the other characters show their ideas and feelings toward Boo. It shows the relationship between Boo and the children taking shape. The moment is an important plot point within the story.