The hen house is a building made specifically for hatching chickens. It produces eggs and chickens for food. Chickens are the only animal that are able to be farmed in the game. There is a chicken coup in the corner opposite the main entrance, four nests for hatching chickens, and a little pen for the chickens to go out and get slaughtered. It can also be used as a shelter if you get caught in a storm.
Interestingly, it does not require eggs to craft, allowing you to farm chickens without a trip to mainland. It seems to be an upgraded version of the chicken coup, seeing as it automatically spawns eggs and chickens. Due to the fact that chickens spawn here, and chickens drop feathers upon death, it can also be used to farm feathers. To maximize your chicken output without screwing up its looks, add 2 more nests on the ground below the shelf with the other nests.