There are four forces acting on the plane...

Weight = inherent property of the plane and you you you, it also helps to bring the plane back to te ground!!!
Lift = the forces needed to lift the plane off the ground by countering the weight
Thrust = push the air backward and as a result, propel the plane forward
Drag = resistance that has to be overcome by the thrust force

To generate thrust, all u need is to push the air backward and from newton's law that every action has a reaction, the air pushes the plane forward... And a propellor or a jet engine does just that... Pushes the air backward...

To generate lift, u need an aerofoil and air movement... Or position the wing in a way that it attacks the air at an angle... As explained by earlier poster, the pressure difference generated by air accelerating over and under the foil causes a upward lift... So the critical part is that u need air movement over the aerofoil... but all u need is a RELATIVE movement!!! And the propellor helps pushing the air over the foil... As we can't depend on natural wind to do just that...

To take off, u need to generate an upward lift that is greater than the weight... Hence, u have to force air backward to a critical speed so that the required lift is generated... But as a result of pushing the air backward, u get a forward movement... U can't destroy the plane forward movement... And to solve that, u add wheels so that the plane can run on the runway till it is completely off the ground... So as mentioned by a lot of posters earlier, the wheels doesn't generate any thrust... It is merely an aid...

So, in the show... It is the usual take off approach... In reality, the wheels roll and the runway is not moving... What they did or tried is to improvise a "runway" that is moving backward at the same speed of the plane so that the plane appeared to be stationary (they tried but they failed, coz they can't control the speed that well)... It is again the relative speed or movement we are talking about... There is still air movement over the wings... coz the propellor is still pushing the air backward... But the forward movement of the plane is prevented/countered by the conveyor belt moving backward... So that the plane appeared to be stationary...

Oh, i have to mention this... I'm not a pilot... But i did stay at Hotel Blah Blah Blah last nite... (i've watched that commercial numerous time... But i can't recall which hotel that is)... Someone help me out here...