You can record explanatory videos, also known as tutorials, in various ways. You can use a screen recording or simply record yourself explaining something.

Another option is the Simpleshow Videomaker - an intuitive application for creating short explanatory videos. There are many different animations available and you can set your video to music yourself or have a computer voice read the script.
As a teacher, you receive a free user account and can also invite students to create or edit a video with you.

You can find a sample video here and a short introduction in the following video.