Much like the former Xbox Live app, Xbox SmartGlass (free) gives you the Xbox 360 Dashboard experience, letting you do things like view your avatar and info, see your friends' bio and game lists, and track and compare achievements.
With this latest version of the app, you get a lot more ways to interact with your console. You now have the ability to type using your iPhone keypad rather than the old hunt-and-peck Xbox controller method; you can browse the Internet on your Xbox using your full iOS keyboard; you can play, rewind, and fast-forward videos; search the Xbox game catalog; send and receive messages from friends, and more. You also have the ability to customize your Xbox avatar using a nifty 3D interface.
The app also hints at more second-screen interactivity with games, movies, and TV shows, but relies on developers to create the content for your device that works in tandem with your console. As new games and shows are released, expect to see more interactivity between the devices in the coming months.
Xbox SmartGlass is free at the iTunes App Store and is a no-brainer for Xbox 360 owners; it gives you a remote connection to your console so you can keep up with messages from friends, game achievements, and discover new content.