The only time Atticus Finch says that something is a “sin” is when he tells his children that to kill a mockingbird is a one. Miss Maude explains to them why he’s so adamant about this:
“Your father’s right,” she said. “Mockingbirds don’t do one thing but make music for us to enjoy . . . but sing their hearts out for us. That’s why it’s a sin to kill a mockingbird.”
These lines introduce one of the main metaphors and the theme of the book: the “mockingbirds” are good, innocent people like Boo Radley and Tom Robinson, and Mr. Underwood says later that killing Tom Robinson is like “the senseless slaughter of songbirds by hunters and children.”
Mockingbirds first appear when Jem and Scout are learning how to use their shiny new air rifles. Atticus won’t teach them how to shoot, but he does give them one rule to follow.
Shoot all the bluejays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird."
And later Miss Maudie says
"Mockingbirds don't do one thing but make music for us to enjoy.”
So, mockingbirds are harmless, innocent creatures, and killing them is wrong, because they don’t hurt anyone. We can extrapolate from this that the mockingbird and Tom Robinson are in the same class of beings.
Like killing a mockingbird, arresting Boo Radley would serve no useful purpose, and would hurt someone who never meant anyone any harm. So over the course of the novel, killing mockingbirds is associated with the sinful, the pointless, and the cruel.
Mockingbirds in the story are representative of innocence. Atticus teaches his children, Jem and Scout, that they don't harm anyone. They just sing their songs. Tom Robinson and Boo Radley represent the two innocent people in the story who are mis represented by the townspeople. Tom, a black man, is arrested for the rape and beating of Miss Ewell. Her father had really done it. Tom is convicted and when trying to escape is killed. Boo is the town's representation of a boogie man. Yet, he is the one who saves the children when Mr. Ewell tries to kill them. In the end of the story the title becomes more apparent when Scout ties the relationship of the innocent Boo Radley to being like a mockingbird.