may be burned, Scout hides her head under Jem's arm.

It may be at this point that Boo Radley places the blanket upon Scout, who is absorbed in the frightening moment. At any rate, she does not become aware of the brown woolen blanket secretly placed upon her shoulders until her father scolds her and Jem for moving from their designated position. After Jem explains that they have obeyed him and not moved, Jem realizes who must have put the blanket on them. Atticus, understanding, agrees that they shouldn't attempt to return it:

"We'd better keep this and the blanket to ourselves. Someday, maybe, Scout can thank him for covering her up."
"Thank who?" I asked.
"Boo Radley. You were so busy looking at the fire you didn't know it when he put the blanket around you."

This solicitous act of the reclusive Boo Radley is not only significant in and of itself; it also foreshadows Boo's heroic act for the children he has come to love that occurs in the final chapters.

Before this point in the story, Boo was known to all of the town, and the neighborhood children, as the "malevolent phantom," a bad character who was responsible for spying in people's windows, harming small animals, and stealing things.  Although none of these things are true of Boo, kids still are afraid of him, and he is a bit of a legend in the town.

As Scout stands outside in the cold, watching Miss Maudie's house burn to the ground, she realizes at some point that she was "clutching a brown woolen blanket" around her shoulders.  She doesn't know where the blanket came from.  It is confirmed by Atticus and Jem that Boo put it there.  She hadn't even noticed.

So, Boo, this supposed evil person, had noticed Scout that Scout was cold, and slipped a blanket around her to keep her warm.  This action symbolizes friendship, kindness, generosity, and, as is a strong theme in this book, how people aren't always what we think they are.  People aren't what they appear to be on the surface, and we shouldn't judge them before we get to know them.  Boo, on the surface a strange social recluse with a reputation for harm, was really a harmless, friendly, kind human being that noticed Scout's need and served her selflessly.  I hope that those thoughts help; good luck!

Boo Radley puts the blanket over Scout’s shoulders because he feels protective of her.

When Miss Maudie’s house catches fire, most of the town comes out to help her.  Atticus tells Scout and Jem to get up, and stations them well away from the fire but close enough to watch.  This means he puts them in front of the Radley house, right by the gate.  After the fire, Atticus notices something odd about Scout.

I noticed Atticus looking at me, first with curiosity, then with sternness. “I thought I told you and Jem to stay put,” he said.

“Why, we did. We stayed—”

“Then whose blanket is that?”

“Blanket?”

“Yes ma’am, blanket. It isn’t ours.” (Ch. 8)

Scout and Jem have no idea where the blanket came from at first.  They were so caught up in watching the men try to rescue Miss Maudie’s belongings at the fire that they didn’t even notice when the blanket appeared.  Nathan Radley was helping at the fire.  The blanket could not have come from him.  It is clear from where they are standing, in front of the Radley gate, that it could only have come from one other source—Boo Radley.

Scout is baffled by this event.  She has spent most of her young life afraid of Boo Radley, and here he was helping her.  It is an unusual interaction to be sure.  Scout doesn’t make the connection with the presents left in the tree.

Jem’s first concern is that Atticus will tell Nathan Radley about the blanket, and that will get Boo in trouble.  Jem knows that Boo considers himself their friend, and that putting the blanket on Scout’s shoulders was just another friendly gesture.  He did it quietly, because he did not want to be seen.  He just wanted to protect Scout.

Although they are not allowed to interact with Boo either, Jem confesses to Atticus that they have had interactions.  He wants Atticus to leave the matter alone.

“…Mr. Nathan put cement in that tree, Atticus, an‘ he did it to stop us findin’ things—he’s crazy, I reckon, like they say, but Atticus, I swear to God he ain’t ever harmed us, he ain’t ever hurt us, he coulda cut my throat from ear to ear that night but he tried to mend my pants instead…” (Ch. 8)

Atticus understands the situation.  He assures Jem that he will not try to return the blanket.  Boo Radley came out that night because, like every other person in Maycomb, he wanted to help.  Too shy to actually take part in the fire-fighting methods, he decided to watch over Scout and Jem. 

This is a turning point in the relationship with Boo Radley for Scout.  There is a long line of evidence that Boo cares about them.  He laughed when they tried to make him come out, he left presents in the tree, and he mended Jim’s pants.  Boo is looking out for them. It’s a good thing too, because if he hadn’t been, he might not have been able to save them from Bob Ewell’s murderous rage on Halloween night.

Boo Radley placed the blanket over Scout's shoulders.

In Chapter 8 of To Kill a Mockingbird, on a bitterly cold night, especially for southern Alabama, Scout is awakened by her father because Miss Maudie's house has caught fire. Since this fire is raging right across from their home, Atticus instructs the children to stand in front of the Radleys' front gate away from the fire.

The fire begins to devour Miss Maudie's house. Finally, the children see the old fire truck, which has been "killed by the cold," being pushed from town by a large group of men. When the men hook the hose to the hydrant, the old hose bursts and water shoots into the air. The men carry out what they can for Miss Maudie, and they call to Mr. Avery to get out.

Shortly thereafter, the fire truck from a nearby town arrives and pumps water on the Finch house and others close by. All that can be done is to protect the nearby homes. It is nearly dawn when the children return to their house. As they enter, a perplexed Atticus looks at Scout; then, he becomes stern, growling, "I thought I told you and Jem to stay put." Scout tries to explain that they have obeyed, but Atticus interrupts, "Then whose blanket is that?" Unaware that she possesses such an item, Scout glances down and sees she has been clutching a brown woolen blanket.

Jem discloses their interactions with Boo and the little things he has done or made for them. This information assists Atticus in his conclusion: 

"We'd better keep this and the blanket to ourselves. Someday, maybe, Scout can thank him for covering her up."
"Thank who?" Scout asks.
"Boo Radley. You were so busy looking at the fire you didn't know it when he put the blanket around you."

Scout is shocked to think that Boo sneaked out of the house to place a blanket around her.

The blanket in To Kill a Mockingbird could represent several things, depending on your interpretation. It could symbolize friendship, generosity, goodwill, or concern. A theme the blanket could represent is that people aren't always what they at first appear to be. It is important to understand the context of where this item appears in the story. As Miss Maudie's house is on fire and the neighbors are trying to save some of her furniture, Scout is waiting outside with Jem in the cold night. Scout doesn't realize she has a blanket draped on her until Atticus questions her. It is determined by Jem that Boo Radley must have draped the blanket over Scout. From there it is also inferred that Boo Radley has made other small gestures of kindness throughout the novel, such as mending Jem's pants and leaving presents in the tree. At first, Boo Radley is viewed as a frightening recluse who never leaves his house. However, despite first impressions of his character, he becomes a symbol of goodness and innocence (though still shrouded in a degree of creepiness). His act of placing a blanket on a child in the cold weather could indicate his compassionate nature and concern for the children.

When Scout comes home from the fire at Miss Maudie's, Atticus sternly asks her where she got the brown blanket that is thrown around her shoulders. It is not one of theirs. Scout is entirely bemused: she has no idea. Finally, Atticus relents and tells her it was

Boo Radley. You were so busy looking at the fire you didn’t know it when he put the blanket around you.

The blanket symbolizes the quiet but active way Boo is looking out for Jem and Scout. He has taken an interest in the two.

Scout, however, is shaken when she finds out that Boo was close enough to her to drop a blanket around her shoulders. To her, he is still the frightening bogeyman.

Boo's gesture is another indication that all is not as it seems on the surface. Scout has to learn to discern between the gossip that circulates in Maycomb and the reality of how people act. The blanket represents the thoughtfulness that characterizes Boo. He is a guardian angel for Scout and Jem, rather than a bogeyman.

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.

One cold night in Maycomb, a huge fire devastates Miss Maudie's house. Scout stands on the sidewalk with Jem watching the fire fighters manfully attempt to deal with the roaring flames. Despite the intense heat of the fire, Scout still shivers in the cold night air. Maycomb has just experienced some rare snowfall, and Scout is not used to these kind of temperatures.

While Scout stands there amidst all the chaos and confusion, someone puts a blanket over her shoulders, but she does not really notice it. When she returns home, Atticus asks her where she got the blanket, but Scout does not have the faintest idea. In actual fact, it was Boo Radley who draped the blanket over Scout's shoulders. Just as he did when he left various keepsakes in the knothole of the tree, he is reaching out to the Finch children, his sole connection to the outside world. In doing so, he is showing once more that he is not the mean, scary boogeyman that everyone thinks he is.

According to dialogue between Scout and Atticus, it is suggested that Boo Radley wraps Scout in the blanket at the scene of the fire. This favor is only one in a string that Arthur
"Boo" Radley is suspected of, as he has placed tokens of goodwill in the knot hole of the tree that Scout and Jem pass every day. Carved figurines, pennies, and candy are just a few of the items that Boo was able to "pass on" to the kids before his father, Nathan, sealed the hole up using cement.

These actions suggest that Boo is not the neighborhood monster as so many of Maycomb's residents have rumored in the past. The kids still have their mysterious superstitions about the Radleys and their house, but Boo's actions in the novel suggest (even before the end) that he is a kind and gentle soul rather than an outcast criminal. 

The night when Miss Maudie’s house burns down, everyone in the neighborhood goes outside to watch the fire that was caused by a cold snap and Miss Maudie lighting a kerosene heater to stay warm.  Atticus shuffles Scout and Jem down the sidewalk away from the fire, and they stand to watch in front of the Radley house.  Scout is so engrossed in the fire that she doesn’t feel the blanket draped over her shoulders by Boo Radley.  This action by Boo shows how tender and caring Boo really is.  Not only does he leave gifts in a knothole in a tree for the children, he also protects them and keeps them safe when he can.  Later, his love for the kids is really shown when he fights the vengeful Bob Ewell who attacks Scout and Jem. 

This incident is just another piece of evidence that shows Boo’s true character.  He is not a ghoulish, insane recluse that the town thinks he is.  His gentle nature really makes him a true symbol of a mockingbird.