The author is stating that the concept of popular sovereignty, which allowed settlers in new territories to decide whether or not to allow slavery, undermined the Missouri Compromise. The Missouri Compromise was a law passed in 1820 that prohibited slavery in certain territories above a certain line of latitude, while allowing it below that line. The introduction of popular sovereignty challenged this compromise by giving citizens in new territories the ability to choose whether or not to allow slavery, rather than following the boundaries set by the Missouri Compromise. This ultimately led to increased tensions and conflicts over the issue of slavery in new territories.
