For anybody interested, the phone app is out on Android now, as well as iOS. You have to download the correct version for your region, for whatever reason.
US:
http://na.finalfantasyxiv.com/pr/special/libraeorzea/EU:
http://eu.finalfantasyxiv.com/pr/special/libraeorzea/It's kind of bare bones right now, but they're supposed to be updating this with more stuff as time goes on.
Right now it has two main features:
- An item database, like XIVDB. Has all the stats of various items, what quests they come from. all the quests in the game, achievements, etc. The item database
works offline. If you don't have a signal or internet connection, it still works.
- Lodestone character stuff. While online, you can get at the character search features of the Lodestone, look at your friends, people's gear, your own gear, etc.
(There's also an "Eorzea Time" clock in the corner, for you cocoon campers.)
Crafting recipes and reverse lookup for those are supposed to be going in a patch soon.

A long time ago they talked about making this app let you manage retainers and the market wards: check what's up for sale, if your stuff has sold, put new items from your retainer on sale as it sells, etc. Hopefully this comes sooner rather than later, cuz that'd be useful as hell.