The principles which allow a Formula 1 car to move are the same that cause an aircraft to fly. The only difference being the wing or airfoil shape is that the airfoil shape will create an upside down producing downforce instead of lift. The Bernoulli Effect means that: if a fluid (gas or liquid) flows around an object at different speeds, the slower moving fluid will exert more pressure than the faster moving fluid on the object. You have probably all heard about that before or seen it on a physics show on the TV, explained in a simpler form. So then the object will be forced toward the faster moving fluid. The wing of an airplane is shaped so that the air moving over the top of the wing moves faster than the air beneath it. Since the air pressure under the wing is greater than that above the wing, lift is produced. The shape of the f1 car uses the same principle. The shape of the chasis is similar to an upside down airfoil. The air moving under the car moves faster than that above it, creating downforce or negative lift on the car. Airfoils or wings are also used in the front and rear of the car in an effort to generate more downforce. Downforce is necessary in maintaining high speeds through the corners and forces the car to the track. Light planes can take off at slower speeds than a ground effects race car can generate on the track. In addition the shape of the underbody (an inverted wing) creates an area of low pressure between the bottom of the car and the racing surface. This sucks the car to road which results in higher cornering speeds which is very important as they are traveling at 200mph. In the last couple years it became really important to have excellent aerodynamics in order to have a chance to compete. Teams that plan on staying competitive use track testing and wind tunnels to develop the most efficient aerodynamic design.
Here are also two videos which explain it again. Once by an expert and in the second video by Niko Roseberg, a german f1 race car driver is explaining how the aerodynamics on f1 race cars work.