They call and leave a message, acting like they've been talking and the start of the conversation just accidentally got cut off. The message then begins as if they've been doing some looking for you or trying to help you in some way for your credit card bills.
After yapping a bit about all the money they're going to save you, because you've been paying only X amount, etc, they tell you that this is the last time they can give you "another" courtesy call. They give you a number to call, and despite the fact that they've been talking as if they are in tight with you, and know all about your finances, they tell you to make sure to have your credit card information / statements / etc. ready and waiting for you to talk about when you call them back.
Something I haven't noticed before, was that one of the calls I received from them was a 'forwarded' call, or so my phone told me it was.
All in all, it's a pretty easy decision -- don't call them back.