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")
While attempting to understand Dathon's metaphorical language in 2368, Jean-Luc Picard wondered aloud if Tanagra was a country. (TNG: "Darmok")
In the script's penultimate scene of ENT: "Fortunate Son", Doctor Phlox recites Voltaire by saying, "A fortunate soldier who serves his country well has no need of ancestors."