They're not called "bounceback" offers anymore, but I don't remember what the new name is.

Sorry about that.
However ... a now-no-longer-called bounceback offer is an offer for a future trip to WDW that you get
while you're in your room at a WDW resort during your trip. The details of the offer are outlined on the offer itself and you
have to book the new offer
before you check out.
All kinds of different discounts/deals have been offered with bouncebacks. The one that was offered while I was at WL 2 weeks ago was for 35% off future stays at Disney Deluxe and Deluxe Villa resorts on particular dates (1/1—1/5/12, 1/8—1/12/12, 1/16—2/8/12, 2/12—2/18/12, 3/4—3/10/12, 3/18—3/31/12, 4/29—5/26/12, 6/3—6/9/12, 8/5—10/6/12, 10/21—11/3/12, 11/11—11/17/12, 11/25—12/1/12 and 12/9—12/15/12). Since this was a room-only discount, the deposit required was for one night's stay.
I pulled the dates off the email that was sent to me while I was at WDW. So, not only was the offer in the room, but they sent me an email, too! And, no!, the email doesn't have the new name that's replaced "bounceback."
HTH.
ETA: I think the offer may be called "Future Stay" offer. Something like that.