If you haven't heard of YouTube Go before, it offers the key features of YouTube along with a lot of data management options. Users can download videos at three different quality sizes and share them with other phones without using any data at all. It also features previews, so you can check out a video before streaming or downloading it. The app itself is less than 10MB, and Google specifically made it work with slower phones with less storage, and it works on much older versions of Android -- all the way back to 4.1 Jellybean, in fact.
In addition to today's big rollout, the app is getting a few new features. User requests have led to a sharing revamp; you can now share multiple videos at the same time, and the feature will now be feature on the app's home page to make the process quicker. Google also enabled high-quality streaming for those times when users have bandwidth to burn. The updated app should be rolling out to many more countries today, but unfortunately Google didn't provide a full list of where it was now available -- your best bet is probably just to check the Play Store.