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.
This part is said in Chapter 10 when Mr. Atticus teaches his children to shoot. He encourages them to shoot tin cans and other objects but adds that killing a mockingbird is sin. Scout is surprised by this saying and she asks Miss Maudie about the meaning of this. Miss Maudie response with this phrase.
Later it becomes a major plot point when Boo Radley who saved Scout and Jem and killed their offenders. Sheriff Tate claimed him innocent though he understood what happened. Scout compares Radley to the mockingbird and considers it a sin to harm him.