A nation-state is a state, or country, that has defined borders and territory. It is additionally a country in which a nation of principally the same type of people exists, organized by either race or cultural background. In the nation-state, generally, everyone would speak the same language, probably practice the same or similar types of religion, and share a set of cultural, “national,” values.
From this strict definition it’s easy to see that the US is not a nation-state. We have multiple ethnicities, numbers of religions practiced, and different cultural norms. Even though citizens of the US share the same borders and territory, we do not, in the sense of the nation-state, share a common nationality.
Another way in which a nation-state cannot exist is when there is a defined ethnic and cultural group that exists without territorial borders, and complete right of ownership to those borders. For example, when immigrants to the US declared the country to be a state, numerous Native American tribes were nations without being states. The borders of the various Native American nations were disregarded by the larger US state, resulting in repeated relocation of these nations to other areas and territories. These territories were only held at the permission of the US. Today, some tribes do have defined borders but they still in some cases may be subject to the laws of the US, making them not fully nation-states.
In fact, most countries do not completely fall within the definition of the nation-state, since most countries have immigrants. Once immigrants come to a country, especially in large numbers, the nation-state can no longer exist. Countries with only a small number of immigrants may still be seen as containing predominantly the same ethnicity and shared culture and may thus be considered as approaching the theoretical nation-state.
Iceland is considered almost an ideal nation-state since immigration to Iceland is quite low. Japan also comes close to being a nation-state because the sense of national identity and shared language is very strong. It is not coincidental that both of these countries are islands and thus less “crossing of the border” can exist.
The Republic of Ireland approaches the nation-state, though immigration to other countries often led to more Southern Irish people living outside of the Republic than inside it. It has relatively few immigrants, except returning nationals or their descendants, and shares a strong national identity. In the Republic of Ireland, the state is founded on the principles of the nation, with laws made respecting the deep Catholic beliefs of the country.
The desire to establish a nation-state can be one of the most devastating ones and may result in either mass eviction of other nationalities or ethnic cleansing. Hitler attempted to establish Germany as a nation-state by first exiling Jews, and then ultimately, by killing the majority of Jewish residents in Germany, and in other countries he conquered like Poland. Attempting to enforce a nation-state where none truly exists often results in high numbers of deaths for large minority populations and a lack of humanity to the extreme.