claiming land in the age of exploration was a big deal to Europe because England, Spain, and France were all fighting for the glory of owning the most property over seas. For those who wanted freedom from the Kings strict rules on religion and speech, this was a gateway for them to "claim land for England" but also a path to their own freedom.
The principle of popular sovereignty is a method used in the 19th century, which states that the people of a given area create and sustain the power of their government through the representatives the people elect. This was enacted during the Kansas-Nebraska Act of 1854, and it was a compromise on the slavery issue that was paramount at the time.