Scout and Jem are young when the book begins. At first, they just see Boo Radley's story as an exciting neighborhood legend. He is the scary monster and mysterious figure. When Dill comes, they act out Boo's story as if it were a movie.
As the children get older, they start to see a different side of Boo. They learn that his is actually a sad story. They also start finding mysterious presents obviously left by Boo, and realize he put a blanket on Scout's shoulders at the fire. When Jem finds his pants mended and left for him, it is another hint that there is more to Boo.
After Boo kills Bob Ewell to save Scout, his true character is finally revealed and Scout gets to meet him and talk to him. She learns that he is kind, gentle and shy.
In the beginning of the novel, Scout and Jem are fearful of Arthur "Boo" Radley. This is due to the fact that they do not have any true understanding of Boo and, because their knowledge of Boo Radley is not based on any personal relationship with him, they fail to recognize his humanity. By the end of the novel, Jem and Scout have come to appreciate and care for Boo as a person.
As the Finch children begin to interact with Boo on a personal level, they lose their fear of him and see his kindness. By the time Boo saves Scout and Jem from Bob Ewell's attack, Scout has become comfortable enough with the idea of Boo's existence as a person to be able to feel comfortable, and even safe, interacting with him face to face.
Scout and Jem feared Boo Radley because he was, in actuality, unknown to them. Once they began to know him and lose their fear of him, they were able to gain some understanding of him.