The Birdcage allows you to store a captured live bird. Once the bird is placed in the cage, it can be fed various things to produce others. For instance, feeding a bird a type of fruit or vegetable will produce Seeds for that particular food which can be planted on a farm to get more. It can also be feed various meats to get Egg which can be eaten or given to the Pig King for more Gold.
Be sure to use a Bird Trap to capture a live bird for your Birdcage.