In Harper Lee's To Kill a Mockingbird, Atticus doesn't specifically give a literal definition of honor. However, he does define courage, and based on his definition of courage and his actions, we can deduce what he sees as honorable.
Atticus gives his definition of courage in Chapter 11, immediately after Mrs. Dubose's death. Atticus informs Jem that he would have asked Jem to go and read to Mrs. Dubose even if Jem hadn't destroyed her camellia garden. The reason why is because Atticus knew she was willfully weaning herself off of her morphine addition, an addiction she had developed through medications prescribed by her doctor for the significant amount of pain she suffered due to her illness. Mrs. Dubose was a very strong woman and had decided she wanted to "leave this world beholden to nothing and nobody." Since her addiction was the only thing left she was indebted to, she wanted to rid herself of it, and she wanted to do so despite the fact that doing so would cause her even more pain and that she would be dying soon regardless. In Atticus's mind, Mrs. Dubose was the "bravest person [he] ever knew" because she set out to accomplish a difficult task despite the fact that her only reward would be death. Hence, Atticus explains to Jem that he wanted Jem to read to her because Atticus wanted Jem to see "what real courage is, instead of getting the idea that courage is a man with a gun in his hand." Atticus then proceeds to give Jem the following definition of courage:
[Courage is] when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. (Ch. 11)
Mrs. Dubose was "licked" by the fact that she would soon be dying but began her difficult task regardless.
Similarly to Mrs. Dubose, Atticus displays courage in his own life by putting his all into defending Tom Robinson. As he explains to Scout earlier, he knows he has no chance of winning Robinson's case. Yet, he is fighting for Robinson's case regardless because he knows it is the right thing to do; he knows that nothing but the testimonies of the Ewells is being used to convict Robinson, and it is unjust to convict a man merely based on testimonial evidence. Atticus knows Robinson's case should not have even been brought to trial since there isn't even any doctor's evidence proving Mayella had been taken advantage of. Based on Atticus's actions with regards to Robinson, we know that Atticus associates doing what is honorable with doing what is courageous. An act is not courageous if it is not also an honorable act. We see Atticus associate his act of courage with doing what is honorable when Scout asks why he is defending Robinson when he knows he'll lose the case, and Atticus responds with the following:
For a number of reasons ... The main one is, if I didn't I couldn't hold my head in town, I couldn't represent this county in the legislature, I couldn't even tell you or Jem not to do something again. (Ch. 9)
Based on the above speech, we know Atticus views an honorable act as one that permits a person to have self-respect and be respected by others. In addition, performing an honorable act can take a great deal of courage; therefore, an honorable act can also be defined as a courageous act.