Twitch is the (new) official app for the service of the same name, which lets you broadcast yourself playing video games, view other players' streams, interact with them, talk with other players, and basically do everything you usually could from your browser.
From this app, you can watch other people playing your favorite games while you chat with other users who are on the same channel as you are.
Besides that, this version of Twitch also allows anyone who starts streaming to monetize their broadcasts. This way, you can make money while you play your favorite games so long as you can get a good following.
The app works perfectly with 3G and WiFi and also lets you change the video quality so it doesn't eat up so much data in case you're using 3G.
Twitch is a very useful app for anyone who frequently uses this service, which you can now carry with you at all times. It's important to keep in mind that THIS is the new version of the Twitch app and that the previous one (version 3.2.3) no longer has official support.