In To Kill a Mockingbird, Calpurnia is one of the fortunate African Americans in Maycomb County in that she is able to read. She also works for Atticus Finch, a lawyer and single father who treats Calpurnia as if she was one of the family. As such, she speaks much like the members of the Finch family when she is there. However, while she is with the members of her own community, Calpurnia uses the dialect of her people so that she will be more readily accepted. She does not want her people, especially members of her church, to think that she is under the impression that she is better than them because of the way they speak. It is a matter of assimilation on Calpurnia's part so that she will be accepted in both communities.
There's an old proverb, stemming from the Bible, that says, "When with the Romans, do as the Romans do". This is the basic premise behind Calpurnia's explanation for why she speaks differently when she is at her church than when she is at the children's home. Calpurnia explains that she doesn't want to seem like she is "puttin' on airs", so she changes her speech to fit into her surroundings. She goes on to explain to Scout that you can't change people or teach them unless they want to change. If people don't want to change, then you have to do whatever you can to fit in with them when you are with them. Lee is doing the same thing here that she does with Atticus's character. Atticus is very laid back and accepting of other people. He doesn't perceive himself as better than others in the town even though he is an educated and talented lawyer. Calpurnia acts in the same manner. Lee shows how differences between people really boil down to minor issues that we should tolerate and adjust to in order to maintain peace and community.
Calpurnia speaks differently in her church to because it would "aggravate" the people there if she spoke the way she does among white people - members would think she was "putting on airs", trying to act better than them (Chapter 12). With this switch, Lee is illustrating the social climate in the 1950's South, and the dual role black people had to play in navigating the vast chasm separating the white and black worlds. Calpurnia has to act a certain way to be accepted by white people - she must conform as closely as possible to their language norms and be proper and subservient. When she is with members of her own race, however, she must speak as they do. The villification from both sides that Calpurnia faces if she deviates from the respective norms is illustrative not only of the divisions between the races but of the antagonism and resentment between them as well.