In Harper Lee's classic novel To Kill a Mockingbird, Atticus Finch gives him son, Jem, instructions regarding his use of the air
Atticus said to Jem one day, '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.'
That was the only time I ever heard Atticus say it was a sin to do something, and I asked Miss Maudie about it.
'Your father's right,' she said. '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.'
Put simply, Atticus does not want Jem to to kill an animal that does no one any harm. Through their innocent songs and presence, mockingbirds bring beauty to their surroundings.
Mockingbirds are symbolic of Tom Robinson, Mayella Ewell, and Boo Radley because each of the three characters is innocent of any real wrongdoing. Each of the three brings a sort of beauty to the town of Maycomb. Tom Robinson's kindness and willingness to help Mayella out of the goodness of his own heart are beautiful; Mayella Ewell brings beauty to the horrible conditions in which she must live by planting flowers, as well as by attempting to find love (although horrible consequences); Boo Radley's leaving the security of his home in order to protect the Finch children, as well as his childlike innocence, are beautiful. The society of Maycomb refuses, in many instances, to recognize the loveliness to be found in Boo, Mayella, and Tom; instead, each is chastised in some way and to some degree.