The "blanket incident" takes place in Chapter 8 on the night of Miss Maudie's house fire. A blanket has mysteriously appeared on Scout's shoulders, and neither of the children can figure out how it got there. But Atticus understands that only one man could have so stealthily placed it there, and Jem soon puts the pieces together as well. When Atticus suggests that they gift-wrap the blanket and return it to its owner, Jem
... seemed to have lost his mind. He began pouring out our secrets right and left in total disregard for my safety if not his own. (Chapter 8)
Scout couldn't follow Jem's response, but Atticus did, "gently" agreeing to let the blanket incident remain a secret, suggesting that one day Scout could thank the owner of the blanket herself.
"Thank who?" I asked. "Boo Radley. You were so busy looking at the fire you didn't know when he put the blanket around you." My stomach turned to water and I nearly threw up... (Chapter 8)
It was only then that Scout realized that it was Boo who had compassionately covered her with the blanket. But Boo had deliberately not revealed himself to the children, preferring to remain their unseen friend. Jem was quick to realize that Boo had not wanted to let the children see him, and Jem recognized that maintaining Boo's anonymity was more important than exposing his actions.