I just ran across another one of these "strength demos" on the Tai Chi E-mail List. I have modified it for a more general audience, it goes like this:
Stand with your back against the wall. Have four or five folks, the stronger the better, get into a line. The first fellow is to lean into your shoulders with his arms extended and locked, with feet together (not braced) palms pressing into your shoulders. The rest of the folks will stand behind each other with their arms on the back of the one in front of them and their feet together (not braced).
You will reach up, grab the first fellow's wrists and use all your strength to push them away. Result: you can't (If you can - add more people! You are probably bigger and stronger than most!). Get your line of folks long enough so that no matter how much strength you use you can't move them. At this point strength is no good to you and you must use something else!
Something else (a.k.a. the hype):
Try it again but this time relax and use your Mind (in Chinese "Yi"), encircle the fellows wrists with just your thumbs and forefingers, put your intent into a distant point straight behind your line of "pressers". Pick an exact spot, mentally consider it and become focussed on it. Then calmly, with intent, extend your arms out to the point on which you have fixed your intent (Yi).
Result: the guys pressing on you will be smoothly sent falling backwards! There is still some physical effort involved, but it is now achieving something because of your intent (Yi)!
Caution: make sure that your pressers do not change their positions between the two tests; you want exactly the same conditions. Also, make sure they each have their feet side by side so that the weight is "dead" (not active); if they are braced with one foot behind, when you do the push with "intention" there is a possibility that they may experience lower back injury. So be careful.
The Secret (a.k.a. the truth):
By placing your back against the wall the exercise limits the use of your waist and legs. So when first presented with the exercise you will quite naturally try to use your waist and legs by pushing against the wall with your lower body. Pushing with your waist against the wall causing your shoulders to come off the wall, which is countered by your hands pushing against the arms of the first guy. Your lower body causes your shoulders to come of the wall, yours arms force your shoulders back against the wall.
When the exercise is change you are then told to "extend your arms" (which is also the secret to Unbendable Arm) you are in the correct position to do the task.
It's a magic trick based on the set-up! It's wonderful!
But, it has nothing to do with using the "Mind" in any special way; it's just a trick of leverage.