To install it you go into the settings of the app and change the setting within the "Beta Participation" menu item to "Steam Beta Update".
This means you can play your Steam games on a PC not tied to your network. For those playing games instead of making them, Steam Link is now officially usable outside of home networks, albeit in open beta.
Valve's announcement of Steam Link Anywhere was pretty short and sweet. It should be added that iOS users are now out of luck, as Apple keep rejecting Valve's attempts to get the app on the App Store.
Game streaming is becoming more and more popular as time goes on.
After you've downloaded the Steam Link app on your Android phone - Apple are still blocking it from sale - your phone will then search for a PC running Steam on the network. Obviously, you'll need a good connection on both devices to make it worthwhile.
Steam Link Anywhere is an extension of Steam Link that will enable users to connect to their PCs and play games from anywhere (thus the name), rather than being limited to a local network. Once that's done, those using Steam Link through Valve's own (discontinued) hardware, Android app, or Raspberry Pi app will be able to connect to a remote computer running Steam. Valve explain the system here, and among the perks for developers are anonymized network traffic (protecting servers and clients from DDOS attacks) and potentially lower pings through Valve's networks.