Teen facilities vary by cruise line and by ship. Some of the more popular ones are Club O2, Optix, Fuel, The Living Room, The Loft, Club Underground and theres 1 more but i forget.
The clubs offer a variety of activities during the day and early evenings, all of which are optional. You don't have to participate.
In the evening the clubs are opened for dancing. Different ships have different policies as far as what kind of dancing is acceptable. I've had ships that strictly enforce a NO GRINDING policy, ones that say it but don't mean it and ones that don't care.
Do a search on the forum for teen clubs, you'll find lots of threads and lots of those have rather legnthy and responses from me. I'll see if i can dig some up.
Also check out the thread entitled "First Time Cruisers: Read This First" also written by me, it'll provide lots of insight into cruising and the teen clubs as well.