Calpurnia is a mother figure to Scout. She serves as both a disciplinarian, as a nurturer, and as a support system. She is also the link that connects Scout to the real Maycomb, or at least to the side of Maycomb (the black side) which Scout would have never known otherwise.
Cal influences Scout in correcting her, for example, when Walter Cunningham was invited to eat at the Finch home. Scout always held a bit of contempt against him for his coarse manners, his poverty, and his ignorance of any better. Since he was demonstrating all these behaviors when he was invited to lunch, Scout made fun of him. Immediately Calpurnia got onto her and demanded that she treated Little Cunningham with the respect that is owed to a guest, and that Scout better not dismiss a person for their current state in life.
Another influence is that Calpurnia loves, limits, and lets Scout be. She does the same with Jem, and with any other person who is honest and connected in any way to the Finches. Calpurnia also always speaks her mind, letting Scout understand that Maycomb is quite a separated place and that things are not as fair as they may seem in the surface.