Both Scout and Jem came to recognize their own faults. They realized that they had held wrong opinions. They both experienced regret and a deeper level of understanding. They both changed after their realizations.
Jem realized that he had had a wrong opinion about their neighbor, the elderly Mrs. Dubose. Jem had treated Mrs. Dubose with contempt. He hated the horrible things she said about his father. He resented that he had to read to her as punishment for chopping the tops off of her camellia bushes. After her death, she sent him a single camellia flower in a box. He became angry and he thought that she had given him the flower to haunt him. Atticus explained the woman's struggles to his son. Jem gained more insight into the woman and he began to understand her. Later, Scout noticed Jem gently touching the flower petals. This showed that Jem's heart had finally softened toward Mrs. Dubose and he forgave her. After that day, Jem seemed to grow up more.
Scout realized that she had feared Boo Radley for no reason. Scout had believed negative rumors about Boo Radley for years. She thought of him as a sort of monster. She considered him to be violent and deranged. Slowly, Scout began to see a new side of Boo. He left gifts for her and Jem in the knothole of an old tree. On the night of Miss Maudie's fire, Boo covered Scout's cold body with a blanket. When Mr. Ewell attacked Jem and Scout, Boo came to their rescue. Scout realized that she had been wrong about Boo. He was not a monster. Instead, he became her friend. She finally understood what a special person he was. Scout reached her hand out to Boo in friendship.