What DuBois means by "life behind the veil" is that black life is invisible in America. Black life is also separate from the lives of others. The word veil as a metaphor. This saying also led to the term "double consciousness" which means that you are always looking at yourself through another persons eyes.
DuBois states that if a person can get out from behind the veil then they will be able to achieve self consciousness. In other words, they will be able to see themselves for who they truly are for the first time.
This is how it is explored in African American literature. The author attempts to explain black life using a veil as a metaphor. Until that veil is removed, blacks will not be able to achieve equality and inner peace.