There are actually two main quotes by Atticus that serve to teach lessons to his children. The first concerns Scout's inability to get along with her teacher on the first day of school. When Scout wants to quit school (after one day in the first grade), Atticus gives her a lesson on tolerance, telling her that she will learn to get along better with people if
"... you consider things from his point of view--until you climb into his skin and walk around in it."
The second refers to the title of the novel. When Scout asks the meaning of another statement that Atticus had made to Jem and her--
"Shoot all the bluejays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird."
--she asks Miss Maudie. Maudie explains that mockingbirds are innocent creatures that only make beautiful music for people to enjoy and who cause no harm to people's gardens or corncribs.
"That's why it's a sin to kill a mockingbird."
The mockingbird is a major symbol in the novel, signifying the human victims of the story who are accused of crimes of which they are innocent.