Popular sovereignty is the belief that people make decisions about laws and their government when a democracy is in place, and the control is ruled "by the people, for the people." Citizens have control, generally through voting for government officials who will represent their best interests.
In other words:
...[it] is the belief that the legitimacy of the state is created by the will or consent of its people, who are the source of all political power.
The concept is linked to social philosophers such as John Locke, Jean-Jacques Rousseau, and Thomas Hobbes in the 1700s. It was also verbalized by Benjamin Franklin who insisted that the government served and answered to the people, and not the other way around. This was seen in the United States when the colonists rejected the sovereign rule of George III of England, replacing him with men they chose to govern colonial America. "Legitimate" government could not exist under a monarch, but must be made up of a government chosen by the people.
This was a crucial element in the Kansas-Nebraska Act passed by Senator Stephen A. Douglas in 1854 while trying to placate the slave owners of the South. Once popular sovereignty became a part of the act, decisions were made based upon what the people wanted, through voting, rather than by the government in passing laws advantageous to their own agendas.