Recently updated to version 2, the $1.99 app allows you to manage friends and friend requests, see who's currently online, compare gamerscores and achievements, and chat over Xbox LIVE messaging to one or more recipients. After logging in with your XBLA credentials, the app will automatically pull down all your friends and other needed account information.
There may, however, be a bit of a caveat emptor required regarding the 360 Live app. As PC World points out, Microsoft stated back in August of last year that apps connecting to Xbox LIVE should be free of charge to end users. Of course, they have to go through Apple to make an appeal regarding particular apps, so it's hard to say what status this $2 app is actually in: if you're hesitating on shelling out the 2 bucks, you may be better off waiting to see if it becomes free. Some sources are also skeptical about handing over Xbox LIVE credentials to third-party developers.