Google's casting platform has been around for a few years now, and Facebook has thus far ignored it. That changes today; after a small test of the feature earlier this year, Facebook has announced official support for casting videos from your phone or desktop. It looks a little different than you may be used to, though.
To cast a video, tap the TV button in the corner of the video frame. Facebook won't use the standard Cast icon, I suppose because this feature also supports Apple TV and other AirPlay devices. When a video is being played on your TV, you can go back to the feed and keep browsing.
This feature is available today on iOS and on the desktop site. It will be live in the Android app "soon." I'm not sure what Facebook's definition of soon is, but it tends to make a lot of changes to the Android app without actually updating it in the Play Store. You may just see casting pop up in the not too distant future.