Alejandro L. answered 04/04/20
Tutor Specializing in Math and History
A "republican", lower case r, government is one in which the running of the nation is of the people's interest. That is, unlike an absolute monarchy or other similar forms of government, the nation and its power effectively "belong" to the people.
The idea of popular sovereignty, especially during the Antebellum Era of US History, was that the people should have the power to decide laws and customs instituted by the government. Back then, popular sovereignty was mostly applied to the legality of slavery. As America expanded west, supporters of popular sovereignty wanted the people to vote on whether or not slavery should be legal in new states. This was opposed to the Missouri Compromise, in which states would be admitted to balance the US Senate between slave and free states.
In essence, "popular sovereignty", is a "republican" ideal, since it stressed that government bend to the will of the people, and not toward political balancing games.