One thing Miss Maudie does more often (and better than other characters) is help Jem and Scout put their father into perspective.
Miss Maudie looks at Atticus with immense respect. His integrity, humility, and strength of character are all things that she sees clearly and that she tries to help Jem and Scout to see. This leads the children to develop an ability to trust their father rather than trusting children on the playground who spread gossip and derision about Atticus and his defense of Tom Robinson.
Miss Maudie is a very good role model for the kids. She teaches them to be respectful of their neighbors (all of their neighbors), appreciate their father, and be brave. When her house burns down, she tells the children it is just stuff.
During the course of the book, Miss Maudie explains what's going on to
Scout and Jem on several occasions. The kids get explanations from their father, Atticus, but we all know that parents' explanations only carry so much weight. When Scout and Jem hear Miss Maudie (who is a female equivalent to Atticus in the story) echo their father's sentiments and beliefs, it helps them understand what's going on around them, and that contributes to their maturation.
Miss Maudie never talks down to Jem and Scout like many of the other women (particularly their other neighbor, Miss Stephanie). Instead, Maudie is their friend, never prying into their private lives or playing "cat-and-mouse with us." She supports Atticus without question, and she tries to ease Jem's and Scout's disappointment and anger following the trial. She explains why Atticus never told them about being a "dead shot" with the rifle, and the children learn that Atticus's humble streak is a positive strength.