Jem’s growin' up. He's gonna want to be off to himself a lot now, doin' whatever boys do, so you just come right on in the kitchen when you feel lonesome. We’ll find lots of things to do in here.

She sounds like the Finches, for the most part, when she is with the Finches. However, when Calpurnia takes Jem and Scout with her to her black church one day, Scout is shocked to hear Calpurnia's speech change when she's around other people of color. Scout says,

I felt Calpurnia’s hand dig into my shoulder. "What you want, Lula?" she asked, in tones I had never heard her use. She spoke quietly, contemptuously.
"I wants to know why you bringin' white chillun to nigger church."
"They’s my comp'ny," said Calpurnia. Again I thought her voice strange: she was talking like the rest of them.

Scout, a child, obviously does not understand why Calpurnia would speak differently in different contexts, but it likely makes sense to the reader. First, as a black woman—especially in this time and place—it benefits Calpurnia to sound like whites when she's around whites. People of color are often seen as suspect by whites, so the more similar to whites Calpurnia can sound, the better for her. However, if she were to continue to talk like whites around her black friends, she would likely be seen as suspect by this community. It benefits Calpurnia to fit in as much as possible with each group, and her speech is a powerful way to achieve this.

Calpurnia's "double-life" is revealed in the two languages she speaks. The languages she speaks are both English, but one reflects the dialect used by white folks in 1930s Alabama and the other reflects the vernacular of the black community. Dialect is defined as the form of language used in a specific region or by a specific group of people, and it can include word choice, word order, slang expressions, and pronunciations. Many responses to this question have already addressed chapter 12, the vernacular she uses while at church, so this post will address her other language.

In this book, dialect is expressed in word choice, order, expressions, and pronunciations. Pronunciations are denoted by the use of apostrophes that shorten or melt together words. For example, where Calpurnia scolds Scout for her rude behavior towards Walter, after her pours syrup on his vegetables and meat. She says,

"There's some folks who don't eat like us, but you ain't called on to contradict'em at the table when they don't. That boy's yo' comp'ny and if he wants to eat up the table cloth you let him, you hear?"

Later in the same scene, Calpurnia says to "hush your fussin'," which could count as an expression reflecting regional dialect. Another expression said by a different character, which reflects the same dialect, is used where Atticus is described as "the deadest shot in the county."

The same regional dialect Calpurnia speaks here is reflected throughout the novel where white characters use words like "I reckon" and "ain't" and "yawll."

Comparing Calpurnia's language and expressions to those of other characters can help readers to understand how she has adopted this dialect, which is not completely academic in word choice and structure (which some readers may mistakenly believe). Remember, dialect is not a reflection of intelligence but of cultural context.

Calpurnia is a member of the black community, but she also fits into the white community in her professional work and friendship for the Finch family. So, she has learned to speak in ways that reflect the regional dialect of both cultural groups, which co-exist, if not harmoniously, in their small town.

Calpurnia doesn't speak two different languages, exactly, but she does speak two different versions of the same language depending on her audience. A term for this phenomenon is "code-switching," which occurs when a speaker uses different manners of speaking at the same time in order to make him or herself understood.

Calpurnia speaks in grammatically correct English with the Finch family, and then when she returns to her own community, she speaks the way they speak, which means she is less concerned with the rules of proper spoken English. Calpurnia can code-switch easily between the two groups of people, and she does so to facilitate communication and to make sure that her connection with her community is intact despite her working for a white family.

When Calpurnia is with the Finch family, she speaks a version of English that white people find acceptable, but when she goes to church with her own people, she speaks as they do. Calpurnia does not want to experience rejection by her employers or her community, which could happen if she did not code-switch. For instance, if Calpurnia's people heard her speaking to them as if they were white, they might feel that she is looking down on them. Potentially because Calpurnia wants to avoid this conflict, she code-switches, as it enables her to protect her different relationships.