The new feature, introduced a few months back, is Battle.net SMS Protect. It's a free service, as long as your mobile phone service provider doesn't charge you to receive text messages, in which case text messages would be charged at the usual rate. SMS Protect cannot use any type of messaging other than text messaging, and doesn't require a smartphone to work -- all your phone needs is the ability to receive SMS text messages, making this a nice feature for those players who don't have smartphones.
There have been mixed reports on whether it works with prepaid mobile phones, but where it hasn't been working that's usually because carriers don't allow the receipt of SMS text messages.
SMS Protect is not designed to replace the authenticator, either the phone authenticator or the physical authenticator. Rather, it is an alert system, designed to warn you about suspicious activity on your account, and allow you to perform certain actions with your phone. Hit the break for more information!
Edit: Zarhym was good enough to drop us a line to clarify the original Customer Support post.
The physical phone itself is not tied to your SMS protect. If you lose your phone, you should be able to get a new SIM card with the same number, and still have access to your SMS protect service. So, you can fix the problem yourself without having to get in touch with customer support. And, as noted, once you've got your SMS protect service back, you can deal with the lost authenticator on your lost phone!
SMS Protect is bound to the phone number and not the physical phone. When a player replaces their phone and hooks it up with their service carrier, SMS Protect will still be tied to that number, much in the same way they'll still receive texts on their new phone from their friends. Unless someone needs to change their number for some reason, this clarified functionality should alleviate most causes for anyone to contact support should they lose their phone.
If you want to find out more about Battle.net SMS Protect, you can check out the FAQ, or watch the video in the header!