A Crown Princess is the heir to the throne of a Kingdom, having either won Crown Tournament, or been the consort and inspiration of the winner of Crown Tournament.
Crown Princesses are different from Territorial Princesses, in that the latter hold lands in Fief from the crown. Both are considered royalty, though the Crown Princesses is higher in precedence than Territorial Princesses.
Crown Princesses exist to allow the heirs a sort of “training period” before ascending to the throne.