What does Calpurnia (Cal) teach Scout throughout "To Kill a Mockingbird"?
First, Cal acts as a mother figure for Scout. For example, after Cal gets after Scout for how she treats Walter Cunningham early in the novel, Scout is angry at her. However, when she returns from school Cal is nice to her and cooks her some crackling bread. In this way she is mothering Scout and disciplining her at the same time.
Second, she acts as a counterpoint to Aunt Alexandra. In the previous example, Cal scolds Scout for embarrassing Walter at lunch. Cal emphasizes to Scout that while she might be of a higher social class than Walter, she still must respect his wishes.
It is no coincidence that later in the book, Alexandra makes an entirely different point. She tells Scout that she is too good to socialize with Walter; Finches don't socialize with white trash. Because of Cal's influence, Scout is able to see both sides of the issue and come to her own conclusion.
Cal also serves to show Scout a different side of Maycomb society. Look at all that Scout and Jem learn when Cal takes them to her black church. She realizes that Cal exists in two different words - a black world at home and a white one with Scout's family. This parallels nicely how Scout is caught between worlds - becoming a young woman and being a tom boy, becoming an adult and still relishing her childhood, being exposed to some of the negative experiences in Maycomb while still being innocent.
Cal teaches Scout never to discriminate against anyone. When Walter Cunningham comes to the house he uses a lot of syrup and Cal tells Scout discriminating against people like this is rude and not everyone is as lucky as they are. She instills good values within the children as the absence of the mother.