The helicopters are a class of aircraft that fly "sucking" air from the bottom and pumping it with a thrust equal to its weight (in the case of hovering, that is, to stand still in air) or with greater thrust (for crawling towards the 'top: climbing).
The movement is generally provided by "direct" the flow of air in a different direction from the vertical. On this page of notes (which gave rise to a much longer article, but still do not know where to publish) we assume for simplicity helicopters "single-rotor" (like what you see in the picture at the bottom of this page).
Bernoulli's Law tells us about the behavior of fluids that given a reference surface (assuming the area "swept" from the rotor head), the sum of the static pressure and dynamic pressure remains the same - in our case, is "above "and" below "the helicopter.
This means that the air velocity in the rotor is greater than the one above the rotor (otherwise we would have an upward pressure, that is, the rotor would push down the helicopter instead of "keep it up" against the force of gravity). For the same reason, the air pressure beneath the blades is also increased (we're still hiring - for simplicity - the column of air that has entered the helicopter at that time).
The air sucked from the rotor will expand back to normal pressure at a higher speed - with simple calculations we obtain a factor of 2, ie the rate of output ("under" the rotor) is twice that of entry.
Because the helicopter can hover must be in balance the thrust force of gravity applied to the mass (commonly - and not entirely accurately - we would say "weight") of the helicopter.
So, given the weight and size of the helicopter rotor, one can calculate the minimum power is needed to balance the force of gravity (ie to keep the helicopter in flight).
We see that if the surface of the rotor increases, the required power decreases (but since the value is under the square root, the decrease is not linear).