Du Bois uses the term double-consciousness only once in The Souls of Black Folk, defining it as:
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. One ever feels his twoness,—an American, a Negro; two souls, two thoughts, two unreconciled strivings; two warring ideals in one dark body.
Later, he discusses this double-consciousness as the state of:
The double life every American Negro must live, as a Negro and as an American ... must arise a painful self-consciousness, an almost morbid sense of personality and a moral hesitancy which is fatal to self-confidence. ... Such a double life, with double thoughts, double duties, and double social classes, must give rise to double words and double ideals, and tempt the mind to pretense or revolt, to hypocrisy or radicalism.
Du Bois does subtly shift his meaning of the concept of double-consciousness to try to explain its complexity. In the initial definition, DuBois is thinking of the ways Black people must adopt an outer self to show to what he calls "American" world that is different from their inner sense of self. In this context, double-consciousness is a burden of having to be both one's self and the self one presents to a world that doesn't understand what one really feels like.
In the second usage, the double consciousness is depicted as entirely an inner, ethical struggle that Black people engage in within their souls. This has nothing to do directly with interacting with whites, but is impacted by the Black consciousness of white thinking and culture.
Common misunderstandings might be to see the struggles of double consciousness in simplistic terms, as simply a "face" of humility or servility that Black people put on in front of whites that disguises their anger or distrust, or to see it entirely as Black confusion that is somehow the fault of Black people. These understandings miss the complex interplay of culture and self that Dubois describes, in which Black people must be smarter and nimbler than whites to survive, always having to juggle two ways of thinking.