A country, nation, or nation-state was a governing entity that was generally smaller than a planetary government, and made up of smaller, states, or provinces, as was found in many instances on Earth.
The United Federation of Planets required that planets have a unified government in order to be considered for Federation membership. However, planetary citizens often felt an attachment to their native region, which may have previously been a nation-state. (TNG: "Attached")
Speculating on other possible outcomes for the Vulcan's first contact with Humans, Hoshi Sato asked rhetorically how the Vulcans knew that their decision to make first contact wouldn't cause other Earth nations to panic. (ENT: "Desert Crossing")