It will allow you to watch (at least some) of the content from Twitch on your big screen TV. This may appeal to Xbox 360 users who would prefer to watch gaming related streaming, shows, and other content on the same big screen that they play games on. Perhaps the intent of this app is so that Twitch can make more of a connection with the users who play games on Xbox 360, and expand their audience. They already have a lot of people using computers to check out Twitch.
The app will have 300 live channels. Users can browse through the directory either by games, featured content, or top channels. The app is Kinect-enabled, so you can use voice or motion commands to tell your Xbox 360 what Twitch channel you want to watch. Right now, the Twitch App for Xbox 360 is available for Xbox LIVE Gold subscribers who live in the United States, only.