What is the significance of this quote from To Kill a Mockingbird: "That Calpurnia led a modest double life never dawned on me. The idea that she...

Calpurnia is considered to be more educated than other African Americans in Maycomb, largely because of her ability to read and the way she speaks. And when they go to the First Purchase African M.E. Zion Church, Scout sees how Cal's demeanor is different from what she is used to. Scout begins to finally recognize that Cal is a real person with a life of her own.

There is a distinct class divide and racial divide in Maycomb.  Due to racial segregation, most African Americans were not given the opportunity to learn how to read in formal educational settings. Calpurnia is different.  She was educated by the Finch household, and most of the time she speaks in the same way as any white person with a formal education.

Your grandaddy said Mr. Blackstone wrote fine English—”

“That’s why you don’t talk like the rest of ‘em,” said Jem.

“The rest of who?”

“Rest of the colored folks. Cal, but you talked like they did in church…” (Ch. 12)

When Calpurnia takes Scout and Jem to church with her, they get a unique glimpse of her life when they are not with her.  She takes part in the African American church activities, but she also speaks like the other African Americans. This is a different speech pattern than Scout is used to hearing from Calpurnia, and they think that she seems to speak two languages.  As part of her "double life," she speaks standard, formal English with the Finches and the African American dialect with her community members.

The Finch children ask Calpurnia why she talks this way when it is not correct.  She explains it to them.

“It’s right hard to say,” she said. “Suppose you and Scout talked colored-folks’ talk at home it’d be out of place, wouldn’t it? Now what if I talked white-folks’ talk at church, and with my neighbors? They’d think I was puttin‘ on airs to beat Moses.” (Ch. 12)

Calpurnia does not want people to think that she feels she is better than them. It is, as Scout acknowledges, the unique speech of her people. It would not be appropriate or comfortable for her to speak to them as she would to a white person.

This quote, and the scene at the church as a whole, demonstrates the ways in which segregation separates and distinguishes people into categories.