Whats the point? Pure convenience.
No, the point is security. Think it through…
How it works now: a complete stranger takes a piece of plastic you hand them and runs it through a machine, often out of your sight. Then, they bring you a piece of paper and you sign it to approve the transaction. You've just handed a stranger your personal credit card number, the security ID on back and given them a signature. Over the course of a month, you might do this what? 10 times? 20 times? 50 times? More?
How it could work: you never hand over anything to make a purchase. You (yourself) use an app on your iDevice that says you want to pay someone for something.
You punch in the total amount to pay them. Your password or thumbprint represents the signature. Money changes hands. Stranger doesn't possess your account number, pin or signature but the same transaction gets done.
THAT's the point. The existing system relies on a big layer of trust. You are trusting that total strangers in often low-paying jobs will not decide to take the information you hand them and make a few purchases for themselves. You've given them all they need to do so and you do it over and over with countless strangers during the course of a month or year.
The alternative "hides" those key bits of information that makes theft by this method relatively easy without significantly changing people's ability to buy & sell. By hiding such info, the ability for the average Joe to commit theft by this method is made much more complicated.
Is it foolproof? No. But it is much better than the current method. Along with hiding the crucial bits of info, the same app can also alert you whenever transactions are being made so you could catch any attempts to charge to your account in real time. As is now, you often find out about such actions days or weeks later, often when the bill shows up and has 2 tickets to Hawaii or other surprises on it.
Why we don't see this as a paramount issue is that the bank typically makes up for the theft by just eating it. You dispute the charge, they can't prove you charged it, so they take the hit. What they would like is to stop taking the hit and instead shift that to us consumers. However, if they did that with the system as is, not only would there be huge backlash but it might make many of us stop using credit cards. They don't want that. So they're moving down this path of shifting the model from pieces of plastic to hiding the key info via mobile payments.