How do rotorcraft achieve lift?
A vehicle moving within a fluid may control its velocity by reaction, by accelerating a mass of that fluid in a convenient direction, and at a convenient rate. Using a wing is an excellent way to achieve that; birds and airplanes are able to fly by using wings that accelerate air down- and rearwards, and a propeller is nothing but a set of slender wings attached to a rotating hub.

In order to achieve a given thrust, that propeller must have a convenient size, and has to rotate at a high enough speed, so that it accelerates a mass of air and the change of momentum of that mass of accelerated air is transformed into a force that we call thrust. The magnitude of that change of momentum is proportional to the mass of air moved and to its change of velocity.

The rotor of a helicopter is just a large propeller that accelerates air downwards (and also rearwards, and sideways too, by means of a control called 'the cyclic')