Dill, Jem, and Scout, during their Summer role-playing games, made the Radleys and specifically Boo, a subject of a myriad of imaginary legends. Everything from him attacking his unsuspecting mother, to poisoning nearby fruit trees, you name it.
The truth was that he was mentally handicapped (challenged), and his family protected him and isolated him the way people tend to do with birds.
However, he was not the only mockingbird in the story. Tom Robinson was his doppelganger. Both men had limitations, and both had to fight to defend themselves against the machinations of society. That is reason enough to see how they both parallel mockingbirds: A bird that mocks the songs of other birds (and might get a bad rap about it) simply because it has an innate limitation to create its own song.
In the text, mockingbirds are referred to as not doing anything bad, but singing beautifully. It says they do not nest in corn cribs or eat things they aren't supposed to. They are completely innocent creatures.
If you were to take a look at Boo Radley, he does nothing bad. There are many who rumor that he does bad things, but those things simply aren't proven in the book. Boo Radley is an innocent character too who does nothing but one really good thing in the end. I am not sure where you are, just be ready for that.
Boo Radley is the mockingbird of the novel. A mockingbird, as it is explained to Scout and Jem, does no harm to anyone. This species of bird is innocent and exists solely to sing sweet songs to soothe mankind. So to kill a mockingbird would be a very evil thing to do.
Boo Radley, in spite of the bizarre stories that have circulated about him over the years, is really an innocent, shy man, who tries to befriend Scout and Jem in his own way. Plus, he watches out for them and when their lives are threatened by Bob Ewell, he steps up and protects them, killing Bob Ewell. When Scout realizes that her father and Mr. Tate are not going to turn Boo in to the authorities, Atticus asks Scout if she understands why and she replies that yes, it would be like killing a mockingbird - destroying something beautiful and innocent.
Read about it here on eNotes.