First Purchase. The children are astonished and confused when they discover that there are no hymn-books or church programs in First Purchase and find it interesting that the congregation uses a technique called "lining" to sing along. The Finch children also discover that Reverend Syke's preaching style is much different from what they are used to and witness him lock the doors until the congregation raises enough money for Helen Robinson. Jem and Scout also learn more information regarding Calpurnia's background and Scout is astonished to discover that Cal lives a "modest double life." When the children arrive home from visiting Cal's church, they are dismayed to find Aunt Alexandra sitting on their front porch. Aunt Alexandra does not approve of the children interacting with black citizens and attempts to get Calpurnia fired in chapter 14.

I assume that what you are talking about is the part in Chapter 12 where Atticus has to go off to Montogmery.  Since the kids are going to be left alone, he has Calpurnia take care of them.  She brings them to her church for services.

When she first gets them to the church, one of the other members scolds her for bringing white kids to a black church.  But other members are much more welcoming.  By going to this church with her, the kids find out much more about Calpurnia as a person and she becomes more real to them.

Scout and Calpurnia have a teacher-student relationship:

Like Atticus, Calpurnia is a strict but loving teacher, particularly in regard to Scout, whose enthusiasm sometimes makes her thoughtless.

Calpurnia disciplines Scout, and at times, Scout rebels against that teaching. Scout shares her feeling with Atticus who wisely sides with Calpurnia. During one of the times that Calpurnia disciplined Scout, Scout wanted Atticus to get rid of Calpurnia:

'She likes Jem better'n she likes me anyway,' I concluded, and suggested that Atticus lose no time in packing her off.

Scout reacts as a typical child would when she is scolded. In reality, Scout truly loves Calpurnia. Scout is learning. She has to be disciplined, and discipline is grievous. No one enjoys discipline. Calpurnia balances her discipline with affection which often gratifies Scout:

Calpurnia bent down and kissed me. I ran along, wondering what had come over her. She had wanted to make up with me, that was it. She had always been too hard on me, she had at last seen the error of her fractious ways, she was sorry and too stubborn to say so. (3.75)

Truly, Scout is too young to realize that Calpurnia is doing the right thing in disciplining her. Nonetheless, Calpurnia is fair. She scolds or disciplines Scout. Then she will show her tenderness at the right moment.

After Calpurnia had scolded Scout for making negative remarks about the Cunningham boy, the next day she makes a treat for Scout--crackling bread. In a tender moment, Calpurnia shares how lonely she was while Scout was at school:

'I missed you today,' she said. 'The house got so lonesome, 'long about two o'clock I had to turn on the radio.'

Truly, Scout and Calpurnia have a balanced relationship. Calpurnia is balanced in teaching Scout. She scolds using tough love. Then she showers Scout with tenderness and affection. No doubt, Scout will grow up to appreciate Calpurnia for her firm teaching and tender love.

Calpurnia is Scout’s surrogate mother, as Scout’s own mother died years before, when Scout was two. Referring to her mother, Scout writes that she “never felt her absence.” This means that Calpurnia is the only mother figure that Scout has ever known. Calpurnia raises Scout and her brother, Jem, and takes tremendous responsibility and pride in raising them. For example, Scout learns to read and write well before the other children in her grade because Calpurnia has taught her.

Calpurnia is a strict supervisor. Scout says,

In Calpurnia’s teaching, there was no sentimentality: I seldom pleased her and she seldom rewarded me.

Cal is also strict in the rules that Scout and Jem must heed, and Scout frequently thinks that Calpurnia will admonish her for something she contemplates doing (but she usually does it anyway).

Scout loves Calpurnia, although she sometimes wonders if Cal likes Jem better than she likes Scout. Moreover, it would seem that Scout and Calpurnia battle more than traditional mother-daughter pairs do, especially when the daughter is as young as Scout. For instance, Scout explains,

Jem and I found our father satisfactory… Calpurnia was something else again… She was always ordering me out of the kitchen, asking me why I couldn’t behave as well as Jem when she knew he was older, and calling me home when I wasn’t ready to come. Our battles were epic and one-sided. Calpurnia always won…

Moreover, Scout is sassy to Cal in a way that she is not sassy to the other adults in her life, including Atticus. One has to wonder whether Scout’s conduct is because she more time with Calpurnia than with any other adult or if it in some way reflects Scout’s understanding that Calpurnia has a different social status and that Calpurnia works for the Finches.

For instance, one day, she is exasperated with Calpurnia and “suggest[s] that Atticus lose no time in packing her off.” Atticus reminds her of how much Calpurnia does for the family. Most likely, Scout’s suggestion that Atticus fire Calpurnia was said in the heat of the moment and reflected her frustration at the time.

In chapter 12, Atticus leaves town and travels to Montgomery for legislative work. Calpurnia ends up taking Jem and Scout to First Purchase African M.E. Church for Sunday service, where the children get an inside look into Maycomb's black community. The Finch children learn that the majority of the congregation is illiterate, which is why there are no hymn books, and are astonished to witness how the members use a technique called "lining" to sing the hymns. They also watch as Reverend Sykes collects ten dollars to support Tom Robinson's family and discover that Calpurnia lives a "modest double life." Jem is also suprised to discover how Calpurnia learned to read and gains a new respect for her after visiting the church. Overall, Jem and Scout gain valuable insight into the black community after attending Sunday service at First Purchase African M.E. Church in chapter 12.

Atticus is out of town, and Sunday approaches, so Calpurnia decides to take them to her church, because the last time they went to church without Atticus they had gotten into a lot of mischief.  Her solution is to keep them close.  She cleaned them up all nice and took them with.  Here they encounter the surly and confrontational Zula, who accosts them with "you ain't got no business bringin' chite chillunhere-they their church, we got our'n", and Zeebo who steps in to defend them and leads the hymns by singing them first, line by line.  They hear about the collections being taken up to support Tom's wife, and overall, it is a nice little trip.  All of this is in chapter 12; I provided a link with a summary below.

Scout is not happy with Calpurnia in the early chapters.

Our battles were epic and one-sided. Calpurnia always won, mainly because Atticus always took her side... and I had felt her tyrannical presence as long as I could remember.  (Chapter 1)

Scout was particularly angry with Cal after she was punished for being rude to Walter Cunningham Jr. when he visited for dinner.

I told Calpurnia to just wait, I'd fix her; one of these days when she wasn't looking I'd go off and drown myself in Barker's Eddy.  (Chapter 3)

But Scout comes to see the good side of Cal, and she is so impressed with the housekeeper after their visit to First Purchase Church that Scout wants to visit Cal at her own home in the Quarters. Cal serves as a surrogate mother to Scout and Jem, and Atticus is quick to point out to Alexandra that Cal has

"... never let them get away with anything, she's never indulged them... and another thing, the children love her."  (Chapter 14)

Calpurnia has previously taught Scout to write cursive, and she does her best to teach Scout about manners, how to treat guests, and how to serve refreshments to a room full of ladies. Cal keeps an eye on the children when Atticus is absent, setting strict "summertime boundaries" in the neighborhood, and she impresses the kids with her "modest double life" and "command of two languages."

Calpurina helped raise Scout and Jem, and at first Scout sees her only as an extension of herself, which the novel allows for by having Calpurina scold Scout in the beginning. Scout can't imagine Calpurina outside of her household, as being anything other than her Nanny. As Scout slowly begins to grow she realizes that Calpurina is her own person, that she has a life outside of her and Jem. This really comes to a head when Calpurina takes them to her Church. At the Church Calpurina takes on a persona that Scout has never seen, she uses a dialect and voice that is unfamiliar to Scout. Calpurina becomes the link between the black and white world for the children.