Why is there a box floating on top of my other apps?

I'm coming back to Android after many years, and trying to manage Notifications. That's supposed to be accessible by holding a finger on a notification and a menu will pop up allowing you to adjust the app's notification rights. Except something wild happens instead. The menu flashes up for 1/4 second, and then, the undesired app opens in a "half-size window" that floats over my home screen, or anywhere else I try to go. If I click away from it, it "minimizes" and becomes an icon at the top right corner of my home screen. Tapping it there brings back the half-size window. So clearly there's a *cool, productivity-enhancing feature* that I need to be red-pilled on. Can anyone help? - What is it? - Is it inherent to Android, or a trick done by certain apps such as Mod Pizza? - How do I get rid of an unwanted window/icon? - How do I use it as intended? Also, back on the notification screen, am I correct it's a timing thing on the finger-hold? Like "short" = go to the app, "medium" = adjustment menu, and "long" = do the above feature? Can that be adjusted?