From a literary standpoint, Boo Radley—in Harper's Lee's To Kill a Mockingbird—is symbolic. He is like the mockingbirds that Atticus and Miss Maudie find so admirable. The children are told not to harm them because they are harmless, unlike blue jays which are predatory of smaller birds.
In Chapter Ten, Atticus cautions Scout and Jem in using the air rifles they get for Christmas:
I'd rather you shoot at tin cans in the back yard, but I know you'll go after birds. Shoot all the blue jays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird.
Miss Maudie echoes Atticus' sentiments:
Mockingbirds don't do one thing but make music for us to enjoy. They don't eat up people's gardens, don't nest in corncribs, they don't do one thing but sing their hearts out for us. That's why it's a sin to kill a mockingbird.
The premise is that these decent people believe it is wrong to harm the innocent, to harm any sweet and gentle creature. Boo Radley (and Tom Robinson) is that kind of person.
In terms of the plot, Boo Radley—for the children—is a source of mystery. With the imaginations the kids have, especially Jem and Dill, it's no wonder that Boo draws their attention that first summer they are together.
But by the end of August our repertoire was vapid from countless reproductions, and it was then that Dill have use the idea of making Boo Radley come out.
The children try to invite Boo to come out for ice cream. Their favorite game (until Atticus stops them) is role-playing the lives of the Radleys based on fragments of information and gossip they have heard. Ironically, as curious as the children are about Boo, they are a curiosity to him as well. And their time is filled with trying to make sense of the phantom figure of Boo Radley. Boo's concern for the kids is foreshadowed when Atticus realizes that Boo put a blanket quietly around Scout's shoulders the night of Miss Maudie's fire. Boo watches them and laughs at their antics. This shared interest—each in the other—will eventually save Scout and Jem's lives—in that he comes to love the children.
As far as the community is concerned, Boo is either a source of juicy gossip—as with Miss Stephanie—or a source of sadness and empathy for kind-hearted people like Atticus, Miss Maudie and even Heck Tate. When the sheriff realizes that Boo (and not Jem) has killed Bob Ewell, he is worried for Boo's "safety."
I've never heard tell that it's against the law for a citizen to do his utmost to prevent a crime from being committed, which is exactly what he did, but maybe you'll say it's my duty to tell the town all about it and not hush it up. Know what'd happen then? All the ladies in Maycomb includin' my wife'd be knocking on his door bringing angel food cakes. To my way of thinkin', Mr. Finch, taking the one man who's done you and this town a great service an' draggin' him with his shy ways into the limlight—to me, that a sin.
Sheriff Tate wants to protect this "mockingbird."
For the reader, Boo Radley, the ghost-like figure imprisoned during the day and only free to roam about after dark, becomes an unknown quantity until the children are in danger. We aren't certain what has happened till Scout sees Boo in Jem's room—his love of the kids is clear:
A strange small spasm shook him...but as I gazed at him in wonder the tension slowly drained from his face. His lips parted into a timid smile...
Boo is a real person; his love transforms him into an unlikely hero.