The "Negro problem" is characterized by Du Bois as a "veil" that separates black and white consciousness. Black citizens necessarily develop a "double consciousness" in US society in which their own self-perceptions are at war with the way they are perceived by white society.
African Americans therefore become a problem to white citizens because these white citizens refuse to fully accept them as equal human beings, instead marginalizing them as "others." This makes it difficult for black citizens to integrate into American life and a struggle for them to develop a positive self image and strong sense of self. African Americans, Du Bois contends, live double lives, presenting one image—most often the expected image—of who they are to white citizens while living and feeling a very different way.
At the beginning of The Souls of Black Folk, Du Bois mentions being treated as a "problem" for being black. He says that in response to the implied question whites often dance around, he seldom answers:
To the real question, How does it feel to be a problem? I answer seldom a word.
A little later in the introduction, however, he does try to answer the question, by saying it is painful to be considered a problem. This othering makes it difficult for African Americans to find a true sense of identity and worth. He writes:
the Negro is a sort of seventh son, born with a veil, and gifted with second-sight in this American world,—a world which yields him no true self-consciousness, but only lets him see himself through the revelation of the other world. It is a peculiar sensation, this double-consciousness, this sense of always looking at one’s self through the eyes of others, of measuring one’s soul by the tape of a world that looks on in amused contempt and pity.
Du Bois spends much of his book arguing that the way forward for black citizens is not to accommodate themselves to second class citizenship but to fight for full civil rights and equality with white citizens.