I'll respond to this since I'm somewhat familiar with the idea of a nation-state.
The term is made up of the words "country" and "state," first of all. Both may be interpreted in a number of different ways, therefore I will attempt to define what a "state" is today.
In essence, two conditions must be met for a modern state to exist: 1. Territories 2) absolute power over the territory (sovereignty). The absolute monopoly of coercion by the state's ruler over that territory might be interpreted as the expression of supreme authority. For instance, Mexico might be categorized as what political scientists refer to as a fragile state because it lacks the infrastructure necessary to impose the sovereign's will on the northern part of the country, where the cartel is in control. As a result, Mexico cannot enforce its monopoly of power over its entire territory.
You would assume that this is quite self-explanatory, yet before the Peace of Westphalia, there was no such thing as a state (1648).
Now that you know what a state is, let's move on to understanding what a "country" is. First of all, I noticed you claiming in the comment area that Spain isn't a nation-state because there are several countries there. However, you are picturing a different sort of country. The term of a "nation-state" refers to a political entity rather than an ethnic one. not an ethnic country, but a political one. America is a wonderful example since there are many distinct ethnic nations living side by side there, yet they all collectively make up the political country known as Americans.
Their citizenship is American, not "Japanese" or "Mexican," as citizenship is solely a political, not ethnic, concept. In a nation-state, it is the citizens, not the members of the same ethnic group, who constitute the state. Jews, for instance, might become citizens of Poland in this fashion.
Now, using both of these definitions, a nation-state is a state in which the political nation of that country—its citizens—possesses the highest authority (sovereignty).