As a title, "On Being Brought from Africa to America" is about as straightforward as you can get. This poem must be about the speaker's thoughts about being brought as a slave from Africa (West Africa, probably, like Senegal or Gambia—someplace that was not a Christian country at the time) to America. We know she was raised by the Wheatley family, a prominent white family in Boston, and they made sure Phillis received a formal education, and, it sounds like, a formal introduction to Christianity.
Of course, not a one of these biographical details are in the poem, or the title. The title is like an introduction telling the audience what the speaker's going to talk about in her poem. It's almost like she's making an argument to an audience. Throughout the poem, her view is that Christianity is something that saved her, but that also creates racial equality (for, if she can be saved like any other Christian, aren't they all equal?).
Makes sense so far, but how do we reconcile the speaker's feelings about "white society"? Her enslavement eventually led her to Christianity, so she sees that as a good thing, but she's against the white view that black people are inferior. That seems like a contradiction. She claims that it's "mercy" that brought her from Africa to America. So, we could say that, although she was kidnapped and enslaved, it created the environment in her life for "mercy" to enter in and save her from both literal and spiritual slavery.
After all, if she hadn't been enslaved, God couldn't have entered her life. So, although she doesn't condone slavery or racism, she does welcome the change in her heart—and this change is embodied in her message to other Christians and slaves that live in America. In this way, something she hates (slavery and prejudice) brought about something she really loves (Christianity).
The title also introduces the idea of motion, or transference. Just like she uses metaphorical language in the poem, and just like she was converted from being a pagan to a Christian, the title is about movement from one land to another. We noticed that she uses the word "brought," rather than "stolen," or "kidnapped," or "dragged," or any other word that would suggest the struggle that slaves endured as they were taken away from their homeland. This could be because the speaker's tone is positive. She equates her arrival in America as a good thing that brings her to Christianity and God. Of course, it could also be because she's writing as a slave in America, and needs to censor her language in a way that wouldn't be too confrontational.
Finally, you try it, why don't you? What would you name a short essay about your childhood—really short, like eight lines short? That's sort of what Wheatley is doing, only it's a poem about how her life has changed since she was brought over from Africa to America. Although she doesn't typically write about slavery, this poem is front and center about that subject matter.