It's a Japanese-to-English thing. "Hime" is a title for a woman or girl of high social standing. It doesn't directly translate to "princess", but it's often used in a similar context. It could refer to an heiress to a yakuza family, a daughter of a wealthy family, the daughter of a daimyo in the feudal ages, etc. Basically, "hime" applies if the girl is connected in that sort of way.
It just often gets used in a similar sense to the English "princess", even though it doesn't translate that way in a literal sense.
