A communist country is a country that follows the ideals of communism. Communism comes in 2 forms: Economic and Political. Communist countries tend to use both.
Political Communism says that everyone shall be equal. Everyone will have an equal amount of power to everyone. And in the case of property, the government takes all of it, and distributes it as equally.
Economic Communism has everyone working for the same wages, so there is no poor, middle class, or rich. There is a set wage for everyone. The garbage man makes the same amount as the doctor, who makes as much as the fast food worker, who makes as much as the psychiatrist.