Few things that a country needs to classify as a country are as follows:
(1) Legal and Moral right to exist: One of the few things that describe a country is its legitness, a country should have both legal grounds as well as moral grounds to exist.
By legal what I mean is it should be recognized by any form of legal system either from any existing country, group of countries or recognized under international law, although it is not sufficient condition it is a necessary condition.
(2) Should have a territory: A country should have a legit claim on a territory and also should be able to hold the territory.
(3) Must have a governing body: The most important thing to be a country is the presence of a functioning government.
(4) People must have a sense of nationality: Although a country might have a variety of culture and religion people inhabiting the country must put the constitution over their beliefs.
(5) Constitution: A country to be a country should have a constitution that rules over people of that country and must have an enforcing body (Army, police).
Although the above are few points, they might not be complete and need omissions and additions.