Adding a category to a video is one of the steps needed for it to appear in your catalog(the other is it being published).
Navigate to Content > Videos and click the video you want to add a category to. Under the Appearance tab you'll see the Categories section at top and can click the various categories to associate them with this particular video.
A video can appear in as many categories as you like. If you don't have any categories created when you come to this page, click that New Category button to quickly add one.