One of the main new features of iOS 14 is image-in-picture mode, which lets you watch a video in a tiny window while you're doing other things on your iPhone. That would be useful if you, say, wanted to watch a YouTube video in Safari while talking with your friends or checking your emails. Although, alas, YouTube appears to have done everything to stop videos from starting to play while PIP mode is turned on — unless you opt for YouTube Premium, that is.
Just look after yourself. Pull a video on Safari's YouTube page on your iPhone and take it full-screen. If you tap to bring the replay controls up, you should see a picture-in - picture icon in the top-left corner of your screen.
Tap that, and the video would temporarily go to its own window before returning to its regular YouTube site location. And if you want to go back to your home screen when viewing a full-screen movie, you'll see that it flickers quickly into picture-in - picture mode until it disappears.