What is the purpose of the Apiary in Hearthfire?
I see it had bees in it, but they don't do anything.
The Apiary provides you with Bees, Hive Husks, and Honeycombs, all rare-ish alchemy ingredients that can be a pain to acquire in other ways.
Hive Husks in particular, due to a bug, are unavailable for purchase in the base game, unless you also install the Unofficial Skyrim Patch, which fixes the lists and allows them to randomly appear in the inventory sold by alchemy vendors.