After the children get their air rifles for Christmas, Atticus tells them he would prefer they shoot at cans. He recognizes, however, that sooner or later they'll try to shoot birds. He tells them that as fat as he is concerned, they can shoot at all the bluejays they want but to leave mockingbirds alone. He says it is a sin to kill a mockingbird.
Later Miss Maudie explains to Scout that it is a sin because mockingbirds are harmless. They don't get into crops or destroy plants, they just sing.
"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 but one thing but sing their hearts out for us. That's why it's a sin to kill a mockingbird"
This intrigues Scout because she has never heard Atticus describe anything as a sin before. (Of course, for readers it also references the title of the book.)

Atticus views it a "sin to kill a mockingbird because they don't do one thing but sing their hearts out for us."