I believe I can state this better:
its all down to a pressure difference between the air above the wing, and beneath the wing - this is the bernoulli principle: the shape of the wing is such that the topside path is longer than the underside path. the airflow over the top is therefore travelling faster to get past the wing than the air under, so the air pressure is lower, causing lift. in order to best get this, the plane must be moving relative to the body of air. this is also why planes take off into the wind.
therefore, a 'conveyor belt' runway moving in a direction to negate the motion of the aircraft will prevent takeoff - except for this small omission: the wheels dont generate the motion, they just allow free motion: the drive is purely air-based - either a jet or a prop !
Helicopters do exactly the same thing, its just that the 'wings' rotate to produce this pressure difference.
Harriers just do VTO/L by sheer use of thrust. :-)
PS: that was all physics - I did a degree for 3 years, and still like to dabble.