The feature is now in beta and requires a few caveats, but it's still really exciting.
As a software successor to the original Steam Link hardware that Valve killed off at the end of previous year, Steam Link Anywhere allows you to stream any game from your Steam library to whichever of those aforementioned devices you choose.
Game streaming is becoming more and more popular as time goes on.
You'll need to be in the beta branch of Steam to get the update, but you can find instructions on how to enable that here.
As of right now, only Raspberry Pi, devices running Android, and the discontinued but still usable Steam Link hardware can support the Steam Link Anywhere beta.
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. You'll be given a pairing code which you'll need to use to connect with your Steam library on the host PC.
The experience of accessing the pride of your AAA collection will of course depend heavily on how high the bandwidth is on both your PC, and on the device you intend to stream from.
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. However, my T-Mobile data connection at home wasn't fast enough to actually play anything, but I was able to get connected. 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.