W. E. B. Du Bois references this veil in his famous work, The Souls of Black Folk. In it, he discusses the invisible and visible separation that black people endure in dominantly white American society.
The veil itself can represent different aspects of being Black. One is their actual, darker skin color, as if shaded by a physical veil. Another is the unseen "veil" that separates blacks from whites in society. For Du Bois, understanding that he lived inside this veil was a powerful realization. The veil isolated him from white society but also gave him a sense of identity as an outsider to them. To quote:
I was different from the others; or like [them perhaps] in heart and life and longing, but shut out from their world by a vast veil. I had thereafter no desire to tear down that veil ...
By "the others," he means white folks. Although Du Bois recognizes that he and they, as humans, must have some commonalities in their hearts, their worlds are kept separate by this "vast veil." Once he realizes this, Du Bois embraces the veil as an essential part of himself. In the same way as white people held him in contempt, he could do the same for them, because they were not veiled as he was or his fellow people of color were. The veil, therefore, gives him a new sense of connection with other black Americans.