The roll out of Steam Link Anywhere comes at a time when game streaming is on everyone's mind, with Google expected to make some kind of announcement concerning Project Stream at GDC 2019 next week. While the company swiftly killed off production of the original Steam Link box and controller in November of 2018, they have been working in secret on a software implementation of the same concept in the form of Steam Link Anywhere. 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. You could only stream games on your local network at home.
As a software successor to the original Steam Link hardware that Valve killed off at the end of a year ago, Steam Link Anywhere allows you to stream any game from your Steam library to whichever of those aforementioned devices you choose.
Anyone who wants to use Steam Link Anywhere can access it by updating their Steam client to the beta build dated March 13 or newer, Valve said.
Update: Dec. 20, 2018 - Valve is no longer selling the Steam Link hardware, but it will continue to update and support the Steam Link app going forward. 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. The new feature gives users the ability to stream their entire Steam game library anywhere.
Assuming you've got all that covered, you'll see an "Other Computer" option on the screen when searching for computers to connect to via Steam Link.
Steam Link running on Android with the touch controls enabled rather than a paired controller.