I have been following progress of "Link your devices" feature in Google Play Services since a while and things are getting more clear about how its going to work. The latest beta GMS update gives us a glimpse of the setup process and I was able to take some screenshots and video of it. This is still work in progress and have random information such as devices and emails on the setup screen.
Some info about it -
"Link your devices" feature will allow you to connect your multiple devices with the same Google account. For this, Google is using "Device Groups" thing in which you can invite your own device to be added in group. After inviting and accepting the invitation, you will be able to use features such as call transfer and sharing your internet connection to the device which is offline.
What's new -
Most of the changes are related to UI. You will be able to add your existing device and invite other devices from the Google Play Services by going into Settings > Google > Devices and Sharing > Link your devices. You need to be signed in on other devices with the same Google account.
Here are key points from the setup screen -
1. See ongoing video calls on other devices and seamlessly move them here - Initially this thing was not in the feature list when we spotted this feature but Google added it on this setup screen. It is clear from the description that you will be able to switch your video calls from one device to other or move them on your device which you are currently using. For example you receive a video call from your relative on your Android phone but you want a bigger screen for the video call, so you can just transfer that video call to your tablet which is in your device group and continue video calling on the tablet.
2. Share internet access while your other devices are offline - It's all about sharing your internet connection to your other device which is offline. Kind of same thing as hotspot sharing but you don't have to go through the hassle of setup hotspot. I don't know if it will use the hotspot thing or the Bluetooth internet for this. We will see when it's ready.
3. Be the first to get cross-device services when they are released - Google have this cross-device SDK which allows app developers to provide multi-device experience in their apps. Google itself uses this SDK to provide features through Google Play Services. The best example of this feature is Google's Cross-Device services app which allow you to use your Android apps on Chromebook, reply to messages, check status of a rideshare and some other things.
The first screenshot is from the setup screen where you can create device groups and invite your devices to join. You need to accept invitation on other device in order to join it. The second screenshot is from the Google Play Services's "Link Your Devices" settings where you will be able to invite devices as well, in case if you didn't do it on the setup screen.
In the end, here is a video record of the process (Feature is not fully functional yet)