I've used it to put video from web based video chat on top of a full screen video, while still keeping focus on the main video. I mainly browse with a whole bunch of tabs open instead of multiple windows, so it's useful to pull a video out of a page and be able to navigate away and continue watching instead of dragging to a new window which would take up more space and get lost more easily. I've also used it for checking docs while following video tutorials, or watching recorded classes while looking at assignment pages.

It is rare, but sometimes a video embedded in a web page has no option to make it full screen. I can click the PIP button in Firefox, then I can double-click it to make it full screen. Nice workaround for those moments.

I LOVE the picture in picture feature. It's nice for multitasking - I can pull up a video and put it on top of any other full-screen app or webpage.

I've used it when I am multitasking (watching something fun while "working") or while taking notes on the video.

I've run into videos where the option is either to watch a tiny video as-is in the page (too small), or make it full screen (too large), with no in-between option. Twitch clips are an example of this.

If I pop the video out via PiP, I can resize it to a comfortable inbetween size.

I use PiP in Safari, and I find it useful for watching a video in a small window in the corner of my screen without having to keep the page the video was on (YouTube, etc.) open. That way, I can watch the video while reading other tabs, or working in other windows.

It's nice because PiP (at least Safari's/macOS' implementation) keeps the video above all other windows, and it even carries over into other Spaces.

In short: multitasking.

I haven't used it much, but it does allow you to not have to pull a tab out for youtube or the like if you want to watch something on the side while doing something else, and it does it with zero extra interface, which is nice (it's always annoying when I want to resize a video in the window to take almost all the window size and there's useless padding I can't easily bypass).

I use it literally all the time: i watch a video while i do other low intensity stuff, like browsing or messaging.

opening a sports game stream and keeping it on top in the corner while doing something else (my use case)

I use it to make it easy to pass the video only to OBS Studio - the video shows up as a separate window.

I use it for when I want to watch multiple streams of the same event.