A princely state is any state under the reign of a prince and is thus a principality taken in the broad sense. The term refers not only to sovereign nations ruled by monarchs but also to lower polities ruled by various high nobles (often vassals in a feudal system). Such states may be sovereign or not and their reigning 'princes' may actually rule or be reduced in power, as under colonial indirect rule, sometimes becoming mere figureheads.
Specifically, the term "Princely States" (also called "Native States" or "Indian States") was used to refer to sovereign entities of British India that were not under the direct control of the British government but instead entered into treaties directly with the British monarch.