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.