Miss Maudie and Atticus seem to know each other very well and act very jokingly around one another. What is the significance of this?
I agree with sreule's answer. Miss Maudie characterizes the truth for the reader when the lines between truth and gossip get fuzzy. In the movie version of this book, the relationship between Miss Maudie and Atticus takes on a "romantic" twist, but the book never reveals this type of relationship to the reader. At times Miss Maudie's dialogue provides a humorous break in the story. Maudie is a wit and a dramatic foil in the book. Without her, the story would be heavier and perhaps harder to take as the story progresses. When tragedy strikes Miss Maudie in the house-fire, she does not become bitter, but she looks forward to a new, smaller house and a bigger yard for her flowers.
I believe that the relationship between Miss Maudie and Atticus is one of complete trust and friendship that grows over a long time. At one time, maybe in high school, Atticus and Maudie may have been sweethearts, but that time has long past, and they are revealed as good friends. The level of "knowing" between Maudie and Atticus goes beyond words.
Miss Maudie is "different" and like Atticus very smart and intellectual. She can be counted on to stand in for Atticus regarding his children. And, it may be because of the children that we don't know more about their relationship. If there were a romantic liason between the two of them, we don't know because Atticus believed in protecting his children from unnecessary hurts and in discression.
The film version of To Kill a Mockingbird portrays this relationship between Atticus and Miss Maudie a little differently than the novel. So, be careful not to get the two confused. The film portrays a flirtatious dynamic between Atticus and Miss Maudie, but Harper Lee writes their dialogue to show a loyal friendship, not a romantic one.
It is true that Miss Maudie and Atticus make witty comments to one another--I believe that Lee incorporates this to portray Maudie as Atticus's intellectual equal. Atticus lives in a town where many people are provincial or narrow-minded--Miss Maudie is not. Thus, she can serve as a sounding board for Atticus as well as someone who champions his good qualities to his children.
When Atticus or Calpurnia are not around to imbue the children with common sense, Miss Maudie does so. She also becomes a reliable narrator to the reader in the sense that Scout, the novel's main narrator, relates various Maycomb rumors from different sources, but the reader can count on Miss Maudie's version of the town's history and current events to be the more sensible or accurate one.