"The Cave is home to the deadly beasts: Dragonfly, Mightosour and Bearwolf! You can keep your wild Beasts on a tight leash in this chamber."
In the Beast Cave you can raise all the beasts, you can only have one beast in the cave at the time. When a beast is in the Beast Cave you can use it for battle and train it when it's training time.
Beast Cave view
In the Beast Cave you can raise and train all the beasts, here you can see the stats of the beast you are currently training
When you raise a beast you have to train this beast daily, if you don't train the beast it will lose progress. The beast won't lose levels if not trained, it will only lose progress or bonuses.
When you open the Beast Cave you can leash and unleash you beasts. Beasts that are leashed will stay in the Beast Keeper.
Some basic tips on how to train your beasts and how the Beast Keeper works
With the 2013-09-12 update the Tavern was added in the game and in this Tavern you can unlock Wom-Kong the newest beast. This beast can be raised and trained like all other beasts in the Beast Cave.