Today Google has released a new web app for all iOS devices for their music streaming service or locker as some people like to call it. To get to the web app on your iOS device go to music.google.com and you will see the web app. Please know that it is streaming only you cannot browse music catalogs, or upload music into the app.
Google lets you store 25MB of music in your device cache. Content is streamed from your uploaded music collection. When you open the app you can choose what you want to play and then you are taken to something like the window above.
Google Music is currently an invite service (like everything else Google Does) and is currently free for beta testers.