Short answers, pulled from the story.
Sovereignty is the supreme, independent authority to rule and make law over a territory. In political theory, it designates the ultimate legitimate authority over a polity, encompassing both the right to govern internally and the capacity to act independently in international affairs.
Jean Bodin is frequently credited with writing the first European text theorizing state sovereignty, in his 1576 treatise Les Six Livres de la Republique. He argued that sovereignty must be absolute and perpetual, partly in response to the chaos of the French wars of religion.
Stephen D. Krasner identified domestic sovereignty, interdependence sovereignty, international legal sovereignty, and Westphalian sovereignty. These four aspects do not necessarily appear together; a state can be sovereign in one dimension while lacking sovereignty in another.
The Responsibility to Protect agreement, endorsed by all UN member states at the 2005 World Summit, authorizes the United Nations to take action to avert a humanitarian catastrophe within a state when that state's government cannot or will not act. It made explicit that a state's failure to protect its citizens allows outside actors to assume that responsibility, overriding the earlier norm of non-interference.
De jure sovereignty is the legally recognized right to exercise control over a territory. De facto sovereignty is the actual ability to exercise that control in practice, regardless of legal recognition. The two can diverge, as when a government in exile holds legal recognition while another power controls the territory.
In Leviathan, published in 1651, Hobbes argued that people form a commonwealth and submit to a sovereign power to escape a life that is nasty, brutish, and short. He held that sovereignty must be absolute and indivisible, and that if the ruler fails to protect the people, they recover the right to form a new contract.