Early Common Craft videos like this one about wikis used actual paper cutouts that were moved by a hand that you see in the video. Later ones like this one about podcasting use digital cutouts and you don't see a hand in the video. Both versions are effective in communicating big ideas.
You can make your own Common Craft-style videos by using slides and a screencasting tool. In this video I demonstrate how to use Google Slides and Screencastify to make Common Craft-style videos, but you could accomplish the same thing with PowerPoint and Screencast-o-matic.