A city-state is an independent city — and sometimes its surrounding land — which has its own government, completely separate from nearby countries. Monaco is a city-state.
Today, there are only five city-states that are truly self-governing, but in the past this was more common. In fact, well-known cities such as Rome and Athens were city-states, and the entire country of Italy was made up of independent merchant city-states during the Renaissance. These days, government tends to be concentrated in a larger country, rather than split into small, sovereign cities.