Here, Du Bois is useful. "The black man is a person who must ride 'Jim Crow' in Georgia." Which is to say, what makes Harris "black in an American context" is that her phenotype makes her subject to race hierarchy.
It's important too that she has African heritage (by way of Jamaica, a former British slave colony) and that she identifies as black. But all of this is, again, in the context of a system of race hierarchy.
A large part of the story, as well, is that "Black America" has historically been inclusive of many, many people who were not direct descendants of American slaves: Marcus Garvey, Kwame Ture, Shirley Chisholm, Sidney Poitier, Harry Belafonte, etc.
And the reason for this, again, is race hierarchy. Regardless of their national origins, within the United States, they were "Negroes." Thus they lived in segregated environments and were bound in many ways to the fate of those directly descended from American slaves.
And those descendants of American slaves, on the other side, have historically had a pretty capacious view of who is "black" because of the extent to which they are, themselves, a mixed population.
Which is all to say that "Black America" has always been a diverse collection of backgrounds (descendants of US slaves, free-born and immigrants), admixtures and phenotypes.
This includes people on the boundaries, i.e., people who can "pass", whose African ancestry isn't visible in African features. Some people in this category choose to "become white", others don't. A good example of the latter is Walter White, who led the NAACP for 25 years. 
As an investigator for the NAACP, White used his strong European features to his advantage, investigating lynchings in Southern towns while posing as a white man.
A contemporaneous example of the former is Lawrence Dennis, a mixed-race black man who passed as white as an adult and became one of the leading American fascist intellectuals of the 1930s and 40s.
anyway. race. it has no biological meaning! it is socially constructed for the sake of policing the boundaries of a caste system! "Black people" are a national group of African origin defined by a collective experience of racism! "Blackness" has tended to be pretty inclusive!
