In general, I think the best way to answer this is to say that the two kids have a "how the other half lives" experience when they go to the First Purchase Church with Calpurnia. While they are there, they actually see black people living in a "black world." They see (as much as possible) how black people act when they are away from whites.
For example, they learn about the differences in resources available to the races. They see this in how poor the AME church is -- no hymn books, for example. This also brings home how illiterate most blacks are.
Another example is that they see Calpurnia talking like the other blacks do (she doesn't talk that way to them). This starts to teach them about how more educated blacks need to act in the black community.
In general, then, they start to learn more about the details of black life -- this is something they would not have cared about and not usually had the opportunity to see.