It isn't actually a room, but a terrace with a great view observing the interior of Las Noches. When it's not currently in use, the Hougyoku is completely hidden and the terrace appears to be just an ordinary place when Aizen likes to lounge and drink tea. When he needs to use the Hougyoku, he makes its hidden container rise from the ground. Then he can use it to turn Hollows into Arrancars. The terrace is quite spacious, so many of his underlings can observe the process and admire his power. The fact that the place has no walls or roof has another advantage: there are very few things for a newborn Arrancar to smash if he or she isn't content with his or her new appearance.