To understand this, take a look at Bernoulli's Theorem, or the Theory of Flight.
A helicopter rotor blade is simply an airfoil/aerofoil, and looks much like an aircraft wing (in cross-section).
Look at a diagram of a Venturi tube. Air goes in one end, and the SAME quantity of air has to come out the other end (per unit of time, say per sec). A Venturi tube progressively narrows, then progressively widens again. To get through it, the air has to speed up as the tube narrows (since the mass of air entering and exiting per sec is fixed - what goes in one end must come out the other end).
According to Bernoulli, when the flow of a compressible fluid (in this case air) speeds up, the density of the compressible fluid goes down (and vice versa). Pressure is directly related to density, so pressure also goes down when flow rate (velocity) goes up. The lowest pressure is at the narrowest part of the Venturi tube.
An airfoil/aerofoil cross-section can be looked at as half of a Venturi tube. At the thickest part of the chord, the pressure of the air flowing OVER the airfoil (a.k.a. aircraft wing or helicopter rotor) is lowest. This low pressure (relative to the surrounding air) results in a force called Lift. Lift opposes weight, so if you generate enough Lift (if the helicopter's rotors move through the air fast enough), then there is enough upward force (Lift) for the heli to take-off.
Mathematically, Bernoulli's Theorem is expressed (rho) times v = constant.
Here, (rho) is density, v is velocity.