This book is so layered and packed with potential morals that it is very difficult to pick just one. If you have read the book (I hope you have; if not, I highly recommend it. It is one of the best books out there, hands down), then you can understand how it is hard to narrow things down to just one moral. To find a moral that you think fits the book, a useful exercise is to ask yourself some specific questions about the book and its characters. Then, your answers to those questions could work as a potential moral. For example, ponder this question: What would Atticus say is the right way to treat people, whether they are black like Tom Robinson, a creepoid likd Bob Ewell, or a social recluse like Boo Radley? Another possible question: What do we learn about human beings from Boo Radley and how he rescues the children at the end? Here you have a guy that has been put down, judged, analyzed, made fun of, and tormented his entire life; yet, how does he behave at the end? Another question: What are the impacts of racism on normal, average citizens, and what is the best way to combat it? Consider the mob outside the jail for the answer to this one. Also: How does Atticus show true courage as he defends Tom Robinson? Also: Does success mean winning, or doing what is right?
If you answer any one of those questions above, I'll bet that you can come up with a really good moral for the story. I hope that helps to get you started; good luck!
The moral of the book is that you have to do what you feel is right, not what is popular. Every person has his or her own moral compass, and what society considers as right might also be immoral, and what society considers wrong may be morally correct. In Maycomb, defending a black man is considered wrong by most of the society. Atticus considers convicting a black man wrong. Today we side with Atticus, but they would not have then.
The moral of the story is that it is very easy for us to treat other people as if they are not really people at all.
In this book, lots of people get treated as if they were things, not people. Boo Radley gets treated this way. Many of the whites treat blacks this way. This is the sort of thing that Atticus is trying hard to get his children not to do. He is trying to make sure that they realize that all people are people -- all have an equal right to be respected and judged on what they really are.
So this is a novel about treating people the way you would want to be treated -- as a real person who matters.
In Harper Lee's To Kill a Mockingbird, we need only look to the story's title, and Scout's quote at the end of the novel to find the moral of the tale.
Atticus has made it a point to teach the children to put themselves in another person's situation to truly understand that person. He calls it 'walking in their skin.' We can see an example of this when Jem sits and reads to Mrs. Dubose: Atticus is not as interested in punishing Jem for lopping off the tops of Mrs. Dubose's flowers, as enabling him to see Mrs. Dubose in a different light in order to better understand the strength and courage she had, which he never would have perceived through a simple explanation.
In learning to have a care for others, Atticus also presents the most "caring" example he can—situated as they are in a difficult era where people suffered greatly from the scars of the Civil War, to the [deeper] poverty brought on by the Great Depression, and finally to the racial inequities so prevalent then. He speaks of the mockingbird:
Atticus said to Jem, "I'd rather you shot at tin cans in the back yard, but I know you'll go after birds. Shoot all the bluejays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird."
Atticus can abide the shooting of bluejays because they birds that predatorily attack other birds. Scout is amazed by what Atticus says, but for other reasons:
That was the only time I ever hear Atticus say it was a sin to do something, and I asked Miss Maudie about it. "You're 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 one thing but sing their hearts out for us. That's why it's a sin to kill a mocking bird."
Scout especially internalizes this message. When Heck Tate fights for the welfare of Boo Radley (after Bob Ewell is killed), Atticus wants to try to explain the validity of the sheriff's decision regarding Ewell's cause of death. But Scout is way ahead of him.
'Mr. Tate was right.'
Atticus disengaged himself and looked at me. 'What do you mean?'
'Well, it'd be sort of like shootin' a mockingbird, wouldn't it?'
Scout has grown up enough in the course of Lee's novel to comprehend the hardships Boo would face if the townspeople realized what a heroic thing he had done for the children. Scout sees Boo as the mockingbird who didn't "do one thing but sing [his] hearts out for us." She does not want harm to come to someone who causes no harm to others. (As readers we can further relate to this theme: Boo himself is symbolic of a mockingbird, as was Tom Robinson.)
This is the moral of the story: look closely at others to know them— truly know them—and by doing so, make sure to protect those who need to be protected because of their innocence and goodness.
The above is a good answer. I would add that there are a few repeated images/phrases that deserve attention too.
Atticus regularly uses a phrase that means to "walk in someone's shoes". The point he tried to make was that it is important for us to see the world through other people's perspectives before we judge or have our own way about something. Everything we say or do can impact someone else and we should be aware of the reception of our actions.
Furthermore, the image of innocence through the mockingbird regularly occurs. This is portrayed with Tom Robinson's trial and Boo Radley's intervention of the kids' scuffle with Bob Ewell. We are constantly reminded to think of people first as innocent before we jump to greater conclusions.
I think chapters 30-31 clearly show each of these concepts through the treatment and discussion of Boo Radley's character.
The moral of the book is that the world is not good or bad. The world is shades of gray. Like Atticus, some think he is too good to be true and others think he is very realistic. Like Mayella Ewell. She is shades of gray. What she did to Tom Robinson was VERY wrong, but her reasons were that she had no one else to love her. She wanted him to die, he was her evidence that she had done wrong, that she had lied, that a black man was right and she a white woman was wrong. You have to keep in mind their level of respect for people of different races. So for her being a white southern "lady" she thought that Tom Robinson should die because she is lying. Mrs. Dubose is shades of gray. She has an addiction which is bad. But she is trying to overcome that addiction before she dies which makes her neither good nor bad. Does that answer your question?