Downloading videos from Facebook on Android can be carried out with FastVid: FB Video Downloader. This application is very simple and it will help you to save those videos that you like so much.
Save the videos that you or your friends share on Facebook.
A video downloader for Facebook
This application turns out to be very useful to create video collections that you can play whenever you want, even when you're offline. It allows you to download videos that you have have shared or uploaded to Facebook and on which you've been tagged. You can also download your friends' videos, of the pages you like or those that have been uploaded in groups.