noun
Refers to a princess of the imperial family; a formal, historical term.
姫御子は宮中で大切に育てられた。
The imperial princess was raised with great care in the palace.
その物語は若き姫御子の冒険を描いている。
The story depicts the adventures of a young imperial princess.
内親王 is a specific title for a daughter of an emperor, whereas 姫御子 is a broader, somewhat archaic term for an imperial princess.
Compound of 姫 (hime, 'princess') and 御子 (miko, 'imperial child'). The exact historical derivation is uncertain, but the term is associated with the imperial court.