Atticus saves Miss Maudie’s rocking chair as an act of kindness toward her. Scout is woken in the middle of the night by her father to learn that Miss Maudie’s house (Miss Maudie is their neighbor) is on fire. All the men run into the house to try to save as much of Miss Maudie’s furniture as possible, but what Atticus chooses to save is her heavy oak rocking chair. Scout asks him about this, and Atticus tells her that he saved the object which Miss Maudie loved the most. Scout understands this; she also knew that the oak rocking chair was the thing that Miss Maudie valued more than her other possessions, as Miss Maudie spent most nights sitting in that rocking chair on her porch.
This scene tells us about each of the three characters: Miss Maudie values the chair because it gives her the opportunity to think and relax and visit with people. Atticus saves the chair because he is a kind man who pays attention to the people around him and is thoughtful about their feelings. The same can be said for Scout, who has also learned strength of character from Miss Maudie, and would want her to have her favorite possession.