What is stadia, exactly?
Stadia is Google's cloud gaming system.
No console. Play on your tv, phone, tablet, etc. That's the general idea.
How it works is that you connect to Google's server and that's where the game really runs. They just stream the video and audio to you.
The version I got comes with a wi-fi controller.
For games, you buy a game, but there's no DVD/CD. And no installation or upgrades. Everything is on the cloud.
So, if it works right, it's pretty amazing.
I've tried it on my tv (via Chromecast Ultra), and on my phone (Pixel 3). No lag, very responsive so far.
It also has the possibility of huger interactions between large groups of players (since they're all really running on the same system)
... AND, I've got a buddy pass that'll give somebody 3 months of Stadia Pro. You don't need a controller or anything else - just play on a Chrome browser on your computer.