In Formula One, slick tires have not been allowed since the 1998 rule changes. The tyres have four circumferential grooves. The regulations specifying that all four grooves be at least 2.5 mm deep and spaced 50mm apart.
The idea was to reduce cornering speeds and increase safety. This is how the groves reduce the grip of the tyres:
The shearing forces on the tread during hard cornering can cause tyre tread 'squirm' if the tread block is too small or too thick. The driver would feel this as a lack of grip. The grooves reduce the block size and the amount of lateral support that the rubber has. This causes the tyre tread to 'shear' more easily. The shearing forces cause the tyre to over-heat, lose grip, and wear out more quickly. To ensure the tyres integrity, harder rubber compounds had to be used, and this reduced cornering speeds.
F1 teams are given two sets of dry weather tyres to use. The tyres with the white grove are the softer set.
More information on tyres at Formula 1
Image from autosport.com