City-State is a city, an independent place, who have their own government. The city-state is a city within another city, where it survives regardless of where it is located, with its own laws.
City-states have existed since Antiquity, as in Ancient Greece, where the most famous were Athens, Sparta and Troy. These cities were within Greece, but they functioned independently, had their own political regime and laws.
In ancient times, the city-states in Greece were called polis, a term used to designate a political system, where these cities exercised sovereignty within the country they were in, and were known to be a political, cultural and economic. It was visible in religion, language, and literature that a city-state was different from the surrounding territory.
The Vatican City, officially called Vatican City State, is located within the city of Rome, Italy, but is a sovereign, ecclesiastical city, ruled by the pope.
Learn more about pope.