It looks as if the individual is blowing right between a cup and the one just above it.
When you blow, what are you doing to the air?
As a hint, if the air is blown between the top cup and the one underneath, it must be the air creating some kind of force to push the cup up and out.
Can you maybe try to give a some kind of explanation on your own now.
PS. You might understand it better by thinking about it some more, than just reading an explanation.
I have been doing quite a lot of tests on my own now and has sort of came to the conclusion that air pressure is forming at the bottom of the outher cup and pushes the inner one up. I tried verfiying this by cutting out of the bottom of the outer cup, thinking that this would cause the air to escape underneath. Unfortunately this did not happen to be the case.
By cutting out the bottom of the outer cup, did not the air flow out the bottom or was it not able to.
Tried it myself with poking holes in the bottom of paper cups, and the top cup still wants to pop up.