Popular sovereignty is a Constitutional principle that, for a long time, stood in the way of African Americans gaining equal rights.

Popular sovereignty is the idea that the majority of people should rule.  Their ideas and values should be enacted into law.  The problem is that this can perpetuate discrimination and segregation.  The majority of people in Southern states wanted to discriminate against African Americans.  Following popular sovereignty, discrimination and segregation were established as matters of law.  

In this way, popular sovereignty blocked African American attempts to gain rights.  Later, of course, popular sovereignty granted rights to African Americans when Congress (elected by the people) passed laws such as the Civil Rights Act of 1964.