What is a country's freedom from outside control?

It is known as sovereignty, which means that the country, or State as it is also called, has rights that are not given to parties outside its borders. This implies that a country, (state) has the final say and control over what happens inside of itself.

To try and use an example of the United States and its Constitutional Republic:

From the Declaration of Independence through the Articles of Confederation and then the Constitution You are the sovereign controller of your body, from there if you own a piece of land you have 'sovereign' authority over that land. Then the group of land owners that make up a town have 'sovereign' control over the town to which they agree to give a piece of their control temporarily over to people that will handle the everyday business of the town. As well do the land owners of the City. All the land owners of the town's and cities that make up the State have sovereign control over that and temporarily give up a portion of that power to a group of people to do the day to day affairs of the state.

Now in America's case the 50 countries (states) together decided to give up certain rights, temporarily, to a group of people (federal government) to protect the entire 50 states from outside intrusion (enemies), to work on foreign trade as a whole, which gives the individual states more bargaining power and as well to guarantee free and unobstructed trade and travel between the individual states, (countries) of the United States.