There are many reasons for downloading a video. If you are on a metered service, you might want to download videos during off-hours when the rates are cheaper. You might want to watch videos where the bandwidth doesn't support streaming, or you might just want to make certain that you always have that video of cute cats to show your friends.
Downloading a video from the Internet
Getting ready
One program for downloading videos is youtube-dl. This is not included in most distributions and the repositories may not be up-to-date, so it's best to go to the youtube-dl main site at http://yt-dl.org.
You'll find links and information on that page for downloading and installing youtube-dl.