The Oooku (or often alternative romaji - Ōoku) is the location of the Edo Castle (江戸城,) reserved as living quarters for the women of the Shogun (将軍).
大奥 --おおおく-- (n) shogun's harem; palace's ladies chambers
大奥様 --おおおくさま-- (n) lady of the house
奥 --おく-- (n) interior; inner part; inside

Oooku was functioning as female quarters since 1607, established by Tokugawa Hidetada (徳川秀忠), and lasted for about 200 years.

What I find much more interesting is Alternative Universe (AU) manga featuring Japan under matriarchy with the males as the residents of the Oooku and a female shogun. A very smart setting and very interesting switch of gender roles. 大奥 (1) manga by よしながふみ (Yoshinaga Fumi).
My favourite ever double-page spread from this manga:

上様の!
お成り!
上様 --うえさま; うえざま; かみさま-- (n) (1) emperor; shogun; (2) honored person (honoured);
Just so amazingly fabulous! And in 2009 this manga got Tezuka Osamu Cultural Prize.

Magazine モーニング (Morning) issue 08-2009 the cover featured crossover of two mangas -  チーズスイートホーム by  こなみ かなた (Konami Kanata)  and  きのう何食べた? by  よしなが ふみ (Yoshinaga Fumi)

The first is about the adventure of a sweet kitty Chi and the second - a cooking manga about a lawyer who loves to cook and his boyfriend, a hairdresser.

Kenji is jealous over Kakei being sweet to Chi <<<3

Chi is saying おなかすきまちた

Jim Breen offers a dictionary entry:

お腹が空く; お腹がすく --おなかがすく  -- to become hungry; to get an empty stomach