For a non-physicist who's wondered why string theory imagines 10 dimensions--which seems like a totally arbitrary number--the short video above gives a nice visual explanation of why it should be 10 dimensions and not some other number.
That video is basically nonsense and has nothing to do with string theory or physics.
The problem I have with this video, is that while I find it amazing, someone could create a video about 15, 20 or 5 dimensions, and it would still make sens in my mind, with the right explanations.