I have an assignment that requires analyzing characters. The assignment asks how character advances plot, but I am not sure what that means.
The two main elements of fiction are normally plot and character. The plot is the main action of the story, and usually moves from a conflict to a resolution. This conflict is often between a protagonist (the main or leading character) and one or more antagonists (the "bad guy" in genre fiction or movies) who hinders the protagonist from reaching a goal.
Characters in the story can serve to advance the plot, in the sense of doing things crucial to the main action of the story, or they can be peripheral to the plot. Imagine, for example, the story of Cinderella. Cinderella is the protagonist, and her goal is to live a better life. The Prince helps her by offering marriage. The fairy godmother helps her by enabling her to attend the ball. The wicked stepmother and the evil stepsisters are obstacles preventing Cinderella from living a happy life. Thus all of these characters have a role in advancing the plot by what they do or say. There are also characters such as the people attending the ball, who are minor characters, added for realism (you couldn't have a ball without a crowd of people attending), but who have no real role in the plot.
Thus for your essay, you need to look at what each character does to help or hinder the protagonist achieve a goal.