What is the significance of popular sovereignty in the history of the United States?
I think that there are a couple of significant elements to popular sovereignty. On one hand, popular sovereignty is a principle to the United States Constitution. The idea of people being able to vote and have a voice in their government is a significant element to the United States Constitution, forming a critical component of American government. The idea of individuals being able to articulate the course and direction of governmental policy is a part of popular sovereignty and represents one of the most basic principles of the Constitution. Having said this, I think that one can see one of the challenges with popular sovereignty in the years leading to the Civil War. The idea of being able to have citizens exercise popular sovereignty to determine if territories like Kansas and Nebraska should become slave or free territories. Popular sovereignty was conceived as a way to determine the status of these territories, but it was also exposed to be ineffective and even dangerous if not guided properly. While popular sovereignty is a bedrock of the governmental system of the United States, in the years leading to the Civil War it was shown to be a disastrous way to decide issues where intense convictions govern each side. Some issues, as demonstrated, cannot be voted away in hopes of preventing government from taking a leading role in deciding it.
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.
If you are talking about this in the context of the slave issue in antebellum America, the significance of popular sovereignty is that it was an attempt to keep the North and South from splitting apart over the issue of slavery in the territories. However, in many ways, it just made the animosity worse.
The idea of popular sovereignty (a phrase meaning rule by the people) was that the people of certain territories (places that were not yet states) would have the right to choose for themselves whether to allow slavery in their territories. This was supposed to ease tensions by making it so Congress did not have to make that decision.
However, the decision led to a great deal of conflict within some territories. The most famous of these conflicts was the one that occurred in "Bleeding Kansas" as people from the pro- and anti-slavery sides fought one another for control of the territory. This sort of conflict and violence led to further animosity between the North and South--just the result it was supposed to avoid.
Popular Sovereignty was a political doctrine that the United States subscribed during the mid-nineteenth century, which stated that the settlers of a given territory would have the sole right to decide whether or not slavery would be permitted there. The First proponent of this principle was Senator Lewis, who put the idea forward opposing the Wilmot Proviso. But, Senator Stephen A. Douglas was the leading proponent of popular sovereignty in 1854 because he popularized it. The principle Popular Sovereignty was conjured in the Compromise of 1850 and later in the Kansas Nebraska Act that took place in 1854. The events in “Bleeding Kansas” exposed the weakness of the doctrine.