When you first log into the program (after a quick "Blizzard Entertainment" loading screen), you're given a number which you can then use on your Warcraft account management page to associate your phone's authenticator with your World of Warcraft account. We were originally told that you needed a wifi connection from the phone while you did this, but I did it just fine over Edge -- you just need some sort of connection to the 'net. This process takes just a few minutes to do, and once the two are linked, they are permanently linked, and you will need your phone with you whenever you want to log in to your WoW (or any other Battle.net) account. If you ever lose your phone, you'll have to go through Blizzard customer support to get your account back.
If your iPhone ever crashes out and needs to be completely reset (as in, the applications memory must be erased), then it's likely you will have to call support and get your account unlocked as well. This is the majority of the complaints on the app's reviews page in iTunes, and unfortunately, there's no real fix -- Blizzard needs to guarantee that your account stays locked unless you call, so a phone crash will be that much more annoying.
Once you've linked the account and your authenticator app, then the program gets even simpler: all it features is a screen with a number on it that changes every 30 seconds. And when you log into your account, you'll be prompted for one of these numbers. That's it. There is a "resync" button on the screen that will allow you to re-synchronize your number generator with the generator on Blizzard's servers (so that the two match up when you login), but for most cases, that won't be necessary.
You can back off of the "View Code" screen to view a short menu of options, but they are all basically screens of text: Setup will return you to your original code if you haven't yet associated your authenticator with the accont. Help is a short piece of text that basically points you to Blizzard's website for more information,and of course the About screen contains Blizzard's copyright and proprietary information.
So the app itself doesn't do much more than give you numbers -- which is, of course, what it's designed to do. If you already use an authenticator, you might not even need it at all, unless you have an iPhone and think that it would be easier to use that rather than Blizzard's hardware. If you do have an iPhone or iPod touch and haven't been able to get an authenticator, it's probably perfect for you -- not only will you save $6.50, but the small annoyance of having to reset your account in case your phone is lost or broken far outweighs the extra security for your account.
And if you don't have an iPhone or IPod touch, you can either wait for the app to be ported to other mobile devices or hope that you can buy one of Blizzard's official authenticators when they come up for sale again.
The app is barebones as they come (and unfortunately, there's no indication here that Blizzard is doing anything other than the most basic of iPhone programming), but it does what it's meant to, and it will definitely help to lessen the demand of Blizzard's authenticator hardware.