Sovereignty is perhaps the key concept in international law and international relations because it defines the entire way in which countries relate to one another and to international bodies like the United Nations.
To understand this, think about the law within the United States. It is based on the idea that each individual has rights and responsibilites. It is the individual and not (for example) the family that has these things.
Now think about international law. That law is based on the idea that it is the state that has rights and (at times) responsibilities. In international law, the people of a country do not have any rights (to things like freedom of speech) unless their government gives it to them. Governments cannot be told what to do by any higher government unless they have agreed to be told (as in things like Nuclear Nonproliferation treaties).
In this way, the idea of state sovereignty is the basic concept that is the foundation for all international law.