Scout learns many things from Walter's visit. Social codes and caste systems are key issues throughout the novel. This is Scout's first introduction to both of those ideas. First, thanks to Calpurnia's reprimand for shaming Walter when he pours syrup all over his lunch, Scout realizes that there are social guidelines one must follow when company is over. Cal tells Scout: "'That boy's you' comp'ny and if he wants to eat up the table cloth you let him, you hear'" (24)? Cal is trying to impress upons Scout the idea of Southern hospitality.
Scout defends herself by declaring that Walter isn't proper company, he is just a Cunningham, who are one of the poorer families in Maycomb. In this way, Scout has bought into the idea that certain people are superior to others because of their names, histories, and wealth. In terms of a caste system, the Finchs would be near the top and the Cunninghams would be farther down. This is the opposite of what Atticus wants Scout to think. Note too how Atticus treats Walter at lunch, talking about farming with him and treating him properly.
This chapter foreshadows several key events to follow in the novel, such as Scout's ability to diffuse the angry mob that comes to lynch Tom Robinson (see the second link below) and Aunt Alexandra's refusal later in the novel to allow Scout to be friends with Walter because he is white trash (see the final link below).
The theme of the novel is about learning to see things from someone else's perspective. Atticus talks about being in someone else's skin. In the unfortunate events of the first day of school, Scout believes that she is really sticking up for Walter Cunningham by identifying him by his family's poor state. She is bewildered at the idea that she is doing a better job shaming him than the inept Miss Caroline. When Jem invites Walter home, he is trying to give something to the poor boy while restoring his dignity. Scout's ego-centrism is beginning to diminish as she learns the hard way that other people exist and their feelings are legitimate.
Scout's reaction to Walter's unusual eating mannerisms is inappropriate; Calpurnia reacts strongly. Scout is taught that a person's difference does not make him wrong or bad. In addition, Walter's "adult" conversation with Atticus teaches her that looks can be deceiving, and that a lack of material possessions does not indicate that a person in not proficient or unintelligent in practical matters. She is taught to see the value in an individual, rather than form assumptions based on appearance. In addition, she learns to react to unusual circumstances in an appropriate way.