This quote comes from Barack Obama's 1995 memoir, Dreams of My Father: A Story of Race and Inheritance. The quote refers to his struggles as a bi-racial child and adolescent to bridge the two worlds—white and black—that composed who he was, which seemed to be in constant conflict. He discusses the conversations he would have with his black friend Ray about "white folks," as if that culture were not a part of him, and then suddenly would remember his white mother and grandparents. He was half white. Yet it seemed very difficult to him to move from one racial perspective and language to another.
Since he was often perceived as "black" in American culture, Obama struggled with adopting a wholly black identity and felt he couldn't do that. He states in the memoir that his identity couldn't "end there." He believed, as the quote above suggests, that he could use language—"translation"—to bridge the gap between the two cultures; by bringing together the language of the two races he could find a personal identity that would cohere and incorporate all of who he was. This struggle animates his memoir and sends him on journeys, such the one to Africa, to try to form a coherent picture of who he is—from disjointed parts.