A country in EU2 is a political, military, and economic organization. Each country has a monarch, domestic policies, a treasury, etc. All settlements and military units are owned by a country. A country owns one capital province, and may own arbitrarily many other provinces. Each country may have one or more core provinces.
In the game, and in many places on the net, countries are also referred to as "states" or "nations". "State" in its political meaning is a more precise word for the concept. However, unfortunately "state" also has the meaning "status", which is an unavoidable concept in technical description. I find using "state" can be confusing. Therefore it is avoided here except as an adjective, as in "state culture" or "state religion". "Nation" is a word that has come to be mostly synonymous with "state", but it was not true in the EU2 timeframe. Indeed, the development of the nation-state is one of the primary political developments of the Enlightenment.