Google has been busy pushing out updates for its major iOS apps. First was the update to Google Maps yesterday, and the YouTube app gets a change. This is the app's first update since iOS 7 launched, so it includes the expected "iOS 7 compatibility improvements" as well as Accessibility improvements. However, the big new (and much-requested) feature is the ability to choose a clip's video quality over WiFi.
This works in much the same way as choosing playback quality in a desktop browser. Your options will depend on the available resolution(s), but for most clips you should see anywhere from 240p all the way up to 1080p.
YouTube is a free download.