A country is an inhabited geographical area, the limits of which being defined physically (the french-spanish border is the Pyrenees) or ethnically (France is the country of french people).

A state is a more accurate concept defining people living within a particular identified territory, sharing a same rule, and the institutions that rule this territory and its people. 

Sometimes it is possible to interchange "country" and "state", but not always. The U.S.A. are a country and a nation, but not a state, since they're a federal republic of several states. Japan is both state and country.