A
crown princess is a
daughter of a monarch, who also happens to be the
heir to the
throne. In some
monarchies the
firstborn child is the heir
regardless of
gender, and a firstborn girl will therefore
always be crown princess (this is known as
cognatic succession).
In other monarchies sons will have a right to the throne before daughters, and a younger son could therefore be crown prince instead; degrading the former crown princess to princess (known as agnatic-cognatic succession). Finally, a certain few monarchies will have a fully agnatic succession which mean that they do not allow females to be monarchs (or, of course, crown princesses) at all.