I hear a lot that the idea of a nation-state is a primarily European one, stemming from the mid 18th century. However, I've never really understood how it differed from the traditional views of kingdoms or empires. Why would Rome, Medieval England, or Ancient China not be considered nations?
This is a complicated question. Not helped by the shifting definition over time and between languages. Basically, a nation is a people, and ideally a nation would have a state run by, for, and containing the nation.
By this older definition (from the French Nacion), Germany was a nation long before it was unified. It was a nation with many principalities and kingdoms, some of which (cough Austria and Prussia) controlled land that wouldn't be considered part of the German Nation.
I have a great book called Nations and Nationalism since 1780: Programme, Myth, Reality by E.J. Hobsbawm, which I can find if you have any more questions. I'm not clear exactly on what you are confused about.
Quick review: A nation-state is a state run by, for, and containing a nation. A nation is a people. It often is strongly tied to ethnic movements (Germany, post-Yugoslavic Balkans), but a nation doesn't have to be a ethnicity (France, many US Nationalist movements (though the KKK and Black Nationalists could disagree)).