Miss Maudie is like a mother figure to Scout. Scout enjoys visiting with Miss Maudie particularly when the boys get a little older and begin doing boy things that she can't be a part of. Miss Maudie imparts Scout with wisdom especially in regard to Atticus. Maudie makes clear that Atticus always has the best intentions for his children AND that he is the moral and upstanding character that the town looks toward to do the right thing.
Although near the beginning of the story it seems as if Miss Maudie is a neighbor the kids enjoy taunting, by the end we see a relationship developed enough between Maudie and Scout that only gestures are necessary to communicate. This is clear at the Missionary Society Tea as folks who would like to criticize Atticus or mock Scout don't get away with it as Maudie gives terse but polite reactions in defense or a squeeze of Scout's hand as if to say, "keep your emotions under control". Although Maudie could never be a mother to Scout, she certainly teaches Scout some things about being a woman and respecting her father that Atticus just can't teach on his own. Maudie is a true mentor.
Miss Maudie Atkinson and Scout Finch are neighbors. Over time, they become friends. Scout likes Miss Maudie because she talks to her like she is an equal instead of as a child. Miss Maudie offers Scout mature insights into the problems she faces.
Dill and Jem begin to exclude Scout from their activities. Jem mocks her for being a girl. Feeling rejected, Scout starts spending time with Miss Maudie. Until that time, "she was only another lady in the neighborhood, but a relatively benign presence" (To Kill a Mockingbird, Chapter 5). Previously, Miss Maudie had been friendly to the children and let them roam around on her property. Scout notes that "Jem and Dill drove [her] closer to [Miss Maudie] with their behavior."
Scout enjoys sitting on Miss Maudie's front porch. Together, they talk and observe nature. Scout feels that she can confide in Miss Maudie. Scout asks Miss Maudie about Boo Radley, and the older lady answers her questions with honesty. Scout knows that she can trust what Miss Maudie tells her. She admires Miss Maudie, and calls her "the best lady [she] know[s]." Scout also notes other reasons why she trusts Miss Maudie as a friend:
Jem and I had considerable faith in Miss Maudie. She had never told on us, had never played cat-and-mouse with us, she was not at all interested in our private lives. She was our friend.