Boo Radley is mysterious because no one knows much about him. He has been hiding in the Radley house since he was an adolescent. This was a result of a troubled childhood and possibly, an abusive father. Jem speculates that Boo chose to stay locked up in the house because the people of Maycomb would not accept him. When Boo becomes a recluse, rumors are formed about him and this adds to the speculation and mystery of Boo Radley.
He is mysterious because no one has taken the time to know him, let alone think about things from his perspective. This is one of the main themes of the novel: walking in other people’s shoes. When Scout takes Boo home, she sees the street from his porch for the first time. She literally sees the world from his perspective. Atticus’ line is repeated in the last chapter: “you never really know a man until you stand in his shoes.”
Symbolically, Boo Radley represents the innocence of childhood. When the children are younger, before they learn how the world really works, Boo Radley is their resident monster. As they get older, they lose their innocence when they learn about poverty (though the Cunninghams and Ewells) and racism (through the trial of Tom Robinson and people’s reaction to it). Poverty and racism are the real monsters, and as they are revealed Boo Radley becomes less of a monster. He begins reaching out to the children by leaving them the presents in the tree. He protects Jem from punishment by sewing his pants, and he protects Scout from death when Bob Ewell attacks her.
Boo Radley becomes less and less mysterious throughout the book as the children age and mature. At the end, he comes out. This is the point at which they realize that there are good people and bad people in the world but they are not the ones they thought. Racists are the real monsters. Boo, one of the story’s Mockingbirds, is actually the innocent one. He has been victimized by society, and this is the result of severe abuse from his parents. He is socially stunted as a result.