What did Jem realize after Miss Maudie’s house burned down?

In chapter 8 of To Kill a Mockingbird, Miss Maudie Atkinson's house burns to the ground. As we might expect, the scene is one of chaos and confusion. Scout and Jem can only stand and watch as the flames wreak terrible destruction on Maudie's property. It is winter in Maycomb, and it is freezing cold on that terrible night: poor Scout shivers on the sidewalk.
Later on, when Scout is drinking hot chocolate with Atticus, it comes to her father's attention that she is carrying a brown blanket round her shoulders, one that does not belong to them. Scout has no idea whose blanket it is or how it even got there. Jem realizes that it was none other than Boo Radley, who quietly sneaked out of his house and, amidst all the confusion, gently draped the blanket over Scout's shoulders.
We have reached a point in the story when Boo is increasingly starting to reach out to the Finch children; they are his only real connection to the outside world. He has already placed various objects in the knothole of the tree for Scout and Jem to find. Now he is showing his protective side to the children, which foreshadows his act of bravery later on when he saves them from the evil clutches of Bob Ewell.