What does Scout learn about Calpurnia and the lives of the other African-Americans in Maycomb by visiting Calpurnia's church
Scout and Jem's accompanying Calpurnia to her church opens their eyes to another side of their maid and to the poverty and oppression of the African-American community as well as the personal feelings and tribulations of some of them.
A wise woman, Calpurnia takes Scout and Jem with her to the First Purchase African Methodist Episcopal where the children witness the crumbling tombstones outside in the cemetery, and yet "[I]t was a happy cemetery." The men politely step backwards and tip their hats, and the women cross their arms before them in another gesture of respect. These signs of respect indicate the black community's feelings toward Atticus Finch.
However, one member name Lulu is greatly disturbed by the Finch children's arrival; she accosts Calpurnia, asking her why she has brought white children to their church. "It's the same God, ain't it?" Calpurnia counters in a dialect the children have not heard her use. Then, the children feel the other members closing in on them. But, Zeebo (who is Calpurnia's son), the garbage collector, welcomes them. As the children are seated, they glance around and take notice of the unpainted walls and pine benches that take the place of pews. There is no piano or organ, no hymn books and only cheap cardboard fans to hold in one's hand.
When the Reverend Sykes preaches, he does so more personally than the preachers on the other side of town. Then, he asks for a special collection for Helen Robinson because people will not hire her. Afterwards, he welcomes the children and tells them publicly, "This church has no better friend than your daddy."
After the service is over, Scout asks Calpurnia why she speaks as she does to others at church; she explains that if she does not do this, the others would think she was "puttin' on airs to beat Moses." Scout learns that Calpurnia leads a somewhat double life because the black community differs in many ways from the white one.
This is one of those "someone else's shoes" moments that Atticus has tried to teach to Scout. The people of First Purchase are devastatingly poverty-stricken, yet, rather than drowning in their sorrows, they thrive on their sense of community. They can't even afford hymnals and must simply echo the singer to get through the hymns, but they are willing to lock the church doors and not let anyone leave until they scrape up every last cent to support Tom Robinson's family.
This is a stark contrast to two groups of people: the Ewells and the white church ladies (they come up later in the story).
The Ewells are also poverty-stricken, but rather than use that as an opportunity to support each other and show sympathy, they (especially Bob) are nasty and judgmental. They don't lean on each other at all. In fact, it's likely that Bob beats Mayella, and it's perhaps her desperation for true sympathy and kindness that draws her to Tom Robinson.
The white church ladies sit and talk about how sympathetic they are for the poor and needy, but then in the same breath, they express harsh judgment and criticism, showing some nasty prejudice, especially for other races.
Through her experience at the church, Scout learns what real sympathy and community support is, and she learns that this supportive community loves and believes in her father. She'll see how much they love and respect him in the courthouse once again, but I won't spoil that, in case you haven't gotten to that part yet :-)