Tires are the most important part of race or any car for that mater. (Physics of Racing) After all they are the only thing that is contact with the ground!  Tires work by having a high coefficient of friction.  Some slicks have a friction coefficient grater then 1! (Physics of Racing)  Typical normal street tires have coefficient of about .5 to .6 .  In physics we learned that friction was equal to mew times the normal force.  Since race cars are typical much lighter then normal cars, they use tricks to increase the downward force on the tires.  Some drag tires run really low pressure, other drag cars tune the car to lift the front wheels to put all the weight on the rear tires.  Indy cars use a wing to generate down force, and ventures to suck the car to the ground. (How to Make Your Car Handle)

This is a good example of a slick and a normal street tire.  The little holes on the slick are to check how much slick is left on the tire, since tires tend to ware on the edges faster.  The gaps in the normal tires allow the tire to transfer water away from the tire, so the tire can make contact with the road.  Goodyear makes a slick that is grooved for racing in the rain, but only crazy (Indy, F1) people do that!