The concept is pretty simple, use the existing payments structure which is built around credit cards and create a card that 'cannot' be used for fraud. The latter bit requires some clarification.
So in my use case, I've got vendors who I would like to establish a long term relationship, whether it's a subscription to the WSJ, or a my App Store credit card on file. I give them a credit card number and they keep it on file, I periodically buy services/products from them, and everything is great until my credit card gets compromised some how and then I have to go unwind all of these arrangements with a new card number. Even when I use a 'special' card just for subscription services (easier for me to monitor) if someone breaks into one of my vendors databases "just for the lulz" and my details get out then I still have to go change all my numbers. Its a fact of life but it is also a pain point for me.
What I would like is to have a payments system where I could give the vendor a "credit card" and they could authorize it for transactions. That would send me a text which says "they want to authorize" and if I respond appropriately the relationship is set up. Now if that number gets compromised, the person who gets it can't use it for hotel reservations or 100 pizzas because it isn't authorized to make purchases anywhere except for the vendors where I pre-established a relationship.
Basically getting my card compromised at the LOLCatz shopping cart portal doesn't give the attacker any power other than to spend more than I would expect to spend at the LOLCatz store. My life gets better, the credit card company has less fraud exposure, and I no longer have 'change the card everywhere' firedrills.
As a bonus if this credit card front end could be attached to other payment sources "behind the wall" as it were (imagine having a credit card number that had properties like a Google Voice phone number, it could draw from multiple sources to pay out.) Then I could do even better by attaching 'dubious' cards to an account with a limited withdrawal rate.
I would love to be in charge of my credit like that and I have a much better view over what is, and is not, an attempt at fraud (presuming of course that I am not the fraudster).
I wish some bright YC group somewhere would build something like this.