Although Atticus is a wonderful father to Jem and Scout, they enjoy the company of Miss Maudie because she provides a maternal role for them. She helps to guide them, she cares for them and they can turn to her when they need to. While Calpurnia is maternal towards the children, she is more like a nanny or a grandmother and her experiences of society, as a black woman, are quite different to those of the Finches. Miss Maudie has a more similar social standing to the children than Calpurnia.
Scout particularly enjoys the company of Miss Maudie because she is a strong, female role model, which Scout otherwise lacks. Jem learns about being a man from Atticus, and although Scout learns a lot from her father, he cannot replace the roles played by Miss Maudie and Calpurnia.
Miss Maudie is quite similar to Scout so they are able to identify with each other and they relate to each other as equals. In chapter five, Scout is rejected by Dill and Jem who, being male, choose to play only with each other. Scout says that:
Miss Maudie hated her house: time spent indoors was time wasted.
Miss Maudie teaches Scout about what it means to just be yourself. When she humorously shows Scout her bridgework, Scout says this was:
a gesture of cordiality that cemented our friendship (chapter 5).
This small act is significant in the context of the expected behaviour of Maycomb's women. In chapter one, Scout tells us that
Ladies bathed before noon, after their three-o'clock naps, and by nightfall were like soft teacakes with frostings of sweat and sweet talcum.
Miss Maudie's lack of concern with being a 'lady' allows Scout to feel comfortable in her company, much more so than with Aunt Alexandra who derides her for being a tomboy. In chapter nine, Scout tells us that:
Aunt Alexandra was fanatical on the subject of my attire. I could not possibly hope to be a lady if I wore breeches.
Miss Maudie allows Scout to be herself and does not put any pressure on her, she merely supports her and helps her make the right decisions. For example, in chapter five Scout asks Miss Maudie if Boo Radley is still alive. She says:
What a morbid question. But I suppose it's a morbid subject. I know he's alive, Jean Louise, because I haven't seen him carried out yet.
In her role as a mother figure, Miss Maudie tries to help Scout to develop. She criticises the town gossip about Boo and Boo's mistreatment by his family. This helps Scout to recognise that Boo is not a terrible monster, and like her, is just looking for acceptance.
Miss Maudie is also important in Jem's life as she cares for him and helps him when he is struggling. In chapter 22, Miss Maudie explains the importance of Atticus's defence of Tom Robinson and its impact on the wider community. At his age Jem does not fully understand its significance but Miss Maudie tells him that:
We're so rarely called on to be Christians, but when we are, we've got men like Atticus to go for us...Atticus Finch won't win, he can't win, but he's the only man in these parts who can keep a jury out so long in a case like that. And I thought to myself, well, we're making a step-it's just a baby-step, but it's a step.
For the Finch children, Miss Maudie is more than their neighbour, she is their guardian.