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 select the video you want to add a category to.
Within the Video sidebar, click on the Appearance tab, and you'll see the Categories section at the top.
Select the category you want to attribute to the video or create a new one by clicking on + New Category.
A video can appear in as many categories as you would like.