A nation is a country and its people. It's also the word used for the Native American tribal federations in the US — the Cherokee Nation, for instance — which have their own governments and territories.
Nation comes from the Latin root nat-, which means "born" — the neonatal unit in a hospital is where the newborn babies are cared for. You can also use nation more loosely for ethnic or religious groups: you might speak of "the Jewish nation," meaning not just the country, or nation, of Israel, but Jews all over the world. The Nation of Islam is an African-American Muslim group.