A principality is a land ruled by a prince. It is distinguished from a kingdom, often by being of modest size, sometimes by lacking full sovereignty.
The German term Fürstentum is usually in English rendered as principality.
Liechtenstein, Andorra, and Monaco are European principalities and present-day states.
By contrast, the principalities of Wales in the UK and Asturias in Spain, are not states today, although the independent mediaeval Welsh state was nonetheless referred to as the principality. In both cases, the heir to the country's throne is titular prince of the principality.
Sometimes the notion of a land as a principality is due to historical reasons: Catalonia, for instances, even when it was a sovereign state extending from Barcelona to Athens, was known as a principality, although its ruler was titled king (of the Kingdom of Aragón extended as the Aragonese Empire). It was a curious case where the ruling power had a nominal inferior degree to that of the ruled territory.