Approximately 98% of the videos posted on Facebook are ripped YouTube clips with annoying, aspect ratio-destroying text on the top and bottom, stolen and reposted by some radio station in Ohio that's desperate for social media "engagement." Even so, if you really want to save those videos, the Android app now lets you do so. Kinda. One of our readers spotted the new user interface features and the "Saved" video section in the app, but that word doesn't mean the same thing to Facebook as it does to other folks.
See, "saving" a video on Facebook means it's saved to your account, i.e. to the local copy of the Facebook app. It doesn't mean saving a copy of the video file to the user-accessible file system on your phone or tablet, as happens when Chrome and other browsers save an HTML5 video. Nope, the downloaded file just hangs out in the Facebook app, accessible only from the bloated and annoying interface. I'm no social media expert, but I'm guessing the system is implemented this way so that users can't upload those videos to other services, forcing them to share only on Facebook. If that's true, Facebook has a startling lack of self-awareness.
Videos can be watched offline once saved and removed at any time. It's nice if you have a single video that you want to hang on to and don't have a reliable connection, but otherwise there's not much in the way of functionality. The "save" option is showing up in versions 85 and 86 (beta) of the app.