The authority of a state to govern matters within its own borders free from external interference is known as

What we're talking about here is the principle of sovereignty. A state or nation is seen as having full authority within its own borders. The history of this principle stems back especially to the Peace of Westphalia, which was signed at the conclusion of the Thirty Years War in 1648. The Thirty Years War and other wars of religion in that era included aims by external powers to enforce a particular religion upon kingdoms or principalities that had broken from that religion. When those wars of religion ended without clear winners, the policy of "cuius regio, eius religio" was left standing. That's Latin for, "Whosever region, his religion." In other words, princes and kings were free to establish their own religious policies in their own territories. This principle of sovereignty extended then (and still today) to all matters of governing, not just religious matters. But the history of the idea was very much bound up with the wars of religion of the 16th and 17th centuries.