The princess is the daughter of a monarch, usually a king, and may be seen in role-playing games seated near the king, or wandering about the courtyard. Stories in role-playing games with a princess as a story figure will often revolve around her being betrothed or holding the key to some great power or another.
Outside of the role-playing genre, the primary purpose of a princess is usually to be kidnapped. The hero will be tasked with saving the princess from some great terror, and will often be shown romantic affection from said princess at the end of the quest.
Perhaps the most notable princess is Princess Peach, whose somewhat vapid nature and repeated kidnappings have become a hallmark of the Super Mario series.