The wife of a prince or a woman who holds the office in her own right.
In England, before the Tudor era, there was no female equivalent to princes, dukes, earls, or barons; every female of royal or noble rank below the queen was simply known as "The Lady..."
The vast majority of the female population who is called "princess" is not of royal or noble ancestry... and they probably should count that as a blessing, since royal ancestry does not guarantee power, beauty, intelligence, or any gifts; as pawns in a big political chess game, princesses and queens and noblewomen in general usually had no real power. With a few exceptions, a noblewoman was usually just a manager for the estate and a baby machine for the family dynasty.
The Disney Princess and media portrayals are often highly inaccurate portrayals of royalty; real princesses usually did not befriend commoners and were often married off into other royal families to act as clown cars for their in-laws. Contrary to Disney, any fun and games generally ended at an early age for noble children; they had jobs to do as heirs to family politics. Court intrigue was also a major threat to them and their families; they were never really sure of where their friends and families stood. And as long as she was of royal blood, it didn't matter whether a princess was ugly, stupid, deranged, or sickly; royals marry other royals or nobles, for commoners are generally discouraged (regardless of inbreeding).
Disney's only real princesses are Snow White, Aurora, Ariel, Jasmine, and Pocahontas; Cinderella was either nobility or gentry while the rest were commoners.
The giggly young woman with clothes scrawled with "Princess" in sparkly letters gave little thought to the actual significance of the word. She also had no idea that her Han zi tattoo actually said "prostitute" instead of "princess".