This service is an extension of Steam Link, which allows users to stream games from their desktop PC to a compatible device over an Internet connection.
Last year, Valve retired its Steam Link hardware and shifted focus to a software app, allowing users to enjoy the benefits of Steam in-home streaming on Android and even some smart TVs. I confirmed that I could stream from my gaming PC to my mobile phone using mobile data.
This has changed with Steam Link Anywhere. Once you enable beta participation and pair both devices, you should be good to go. It normally works by connecting a mobile device to a host computer via a local network. After that, all you need to do according to Valve is add a new computer and select "Other Computer" and then follow the pairing instructions that appear before you're ready to get to playing. The app is still officially in beta, but you can try out the service by visiting the Steam Store. This was only really useful for those times when you want to play a game on your couch.
There's still no word from Valve regarding when the cross-platform wide-area game streaming feature will land in a form that isn't beta but that shouldn't come as too much of a surprise. If you have an Android device, you can download it here.
Valve has likewise released the Steam Networking Sockets APIs that are presently accessible to amusement engineers as a component of the Steamworks SDK v1.44 release.