The blades of a helicopter are contoured much like the wing of an airplane. The physics behind both are, basically, the same.
Bernoulli's Effect is usually quoted as the reason behind flight in so many physics textbooks. While this isn't wrong, Bernoulli's Effect isn't actually the main reason that blades/wings can cause flight.
If you've noticed, the wing of an airplane is tilted a bit. This is so that the air molecules hit the bottom surface at an angle. If you have a ceiling fan, you can observe the slight angle in their blades too. This air hits the blade and is rebounded downwards. From the wing/blade point of view, it's being pushed upwards. This is what causes lift.
You can try this, by holding out a piece of cardboard while you're traveling in a fast car. Keep it horizontal and you won't experience lift. Tilt it a bit and you'll feel it being pushed up.
The Bernoulli effect simply adds to this.