Atticus is motivated by personal belief, by the desire to teach his children to be good people, and by the desire to see justice done.
Atticus lives by his own moral code, that does not match the standards of most of Maycomb. Atticus sees everyone as a person, and treats all people with respect regardless of age, race or social class. For example, he is respectful and courteous to his children and other children. He talks to children like adults. He also does not look down on people of other races or classes, contrary to the typical Maycomb belief that "good families" are better than poor ones, whites are better than blacks.
Atticus is also motivated by his desire to teach his children to respect other people, regardless of race or class. He repeatedly teaches his children to respect other adults, and to look beyond the story of a person to find out what that person is really like. For example, he encourages his children to be polite toward the Radley family and Mrs. Dubose. He teaches them that people of other races or social classes are not to be looked down upon by the way he has them treat Calpuria and the Cunninghams.
Finally, Atticus is motivated by his desire to see justice done. He does not accept racism, but he also takes Tom Robinson's case because he believes that Tom is innocent and wants to see him get a good defense, regardless of the liklihood that they will do well at trial. He also wants to repeal the verdict, even though Tom does not believe it will do any good.