While I am not a historian, I study political science and I have studied the rose of the modern-nation-state which is relevant to your question.

Basically medieval and renaissance European ideas mostly viewed "countries" as the holdings of whatever lords or Kings "owned" that land. The idea of a country had not really formed yet. Basically countries didn't exist outside of or independent to political rulers (ie Kings, Queens, nobles, Emperors..) during the medieval age, with the possible exception of city states such as Venice. But these cities had the advantage of strict and real borders: the physical presence of the city. Borders were not sacred boundaries as they are today and as you probably know were frequently shifting. Borders were not thought of in the same way as constituting by themselves a country or state. They depended on what areas you could effectively exercise authority over. It was not odd for borders to be in constant flux for centuries because they didn't conceive of 'countries' as being bound by specific borders.

Borders were simply not conceived of in the same way. Today, even if a country like Somalia becomes a failed state without a government, we still draw it on the map as if it were a functioning state ! This is how ingrained the idea of national sovereignty is to us today. We cannot even conceive of blank borders on a map. Medieval people would not have thought it odd to leave a blank space on the map if nobody controlled that area. They would recognize that some sort of tribes or groups lived there, but if there was no political ruler then a country did not exist.

So originally, the idea of a country as we would think of it today did not exist. Today nearly every country ascribes to the idea of sovereignty, basically that within definite borders political rulers had authority that could not be impeached by other rulers encroaching on it. This was an idea that developed during the renaissance but did not begin to really solidify until afterwards. It is usually said to have been first established by the Peace of Westphalia in 1648 and led by the Dutch Republic which had formed the precursor to the modern state during its Golden Age. The Dutch Republic is a prototype of the state with defined borders that we know today because it dispensed with monarchy and created a republic that actually did have relatively stable and defined boundaries that were not conceived of as land belonging to the monarch. The Dutch began to think of itself as belonging to a specifically defined geographical area regardless of its rulers and their holdings. What also began happening after the Renaissance was an increase in bureaucracy, especially a bureaucracy not exclusively from noble classes, that also contributed to the idea of a bordered country due to administration not being based just on land holdings but rather for the country as a whole, divided into districts not by noble holdings. This is especially notable in France which began developing a state bureaucracy relatively early on in the 1400s and 1500s. This began to change our conception of a country into one with definite borders within which there was only one ruling political authority.

I hope this answers your question