What lessons does Atticus teach his children and how do the lessons help them?
Atticus gives great advice to his children throughout To Kill a Mockingbird, but he also allows them room for independent thought and actions that most kids their age would not enjoy. His advice to step into the other man's skin to understand how he thinks is repeated by both Scout and Jem on several occasions during the novel. He teaches his children to be tolerant of all people--rich or poor, black or white. He is honest and forthright with his children in the hope that they will follow his lead. He leads by example concerning faith in humanity with the expectation that his children will follow suit. He teaches them not to take too much stock in their own family heritage, yet they are still able to understand that some families--such as the Ewells and Cunninghams--are like peas in a pod. Through his actions--not words--he teaches them the definition of humility and gentlemanly behavior.
One of the lessons that Scout learns is an important one in what you might call comportment, or maybe just plain old character. She laments the fact that Atticus is so wimpy in her eyes, he does a semi-wimpy job and he never does anything to show himself as manly or tough. She is really pretty bummed about this.
But then comes the incident with the rabid dog where Atticus demonstrates a steely nerve and people bring up how they used to talk about what a great shot he was. She sees that her father is certainly as manly as the rest but he never makes a show of it. She sees that you don't have to be a braggart or any kind of a publicly tough or powerful person to actually have great inner strength.