Rack and pinion gears are used to convert rotation into linear motion or linear motion into rotation. The rack is the flat toothed part and the pinion is the gear. The diameter of the gear determines the speed that the rack moves as the pinion turns.
A perfect example of a rack and pinion gear system is the steering system on many cars. The driver turns the steering wheel which rotates the gear which then engages the rack so as the gear turns it slides the rack to the right or the left depending on which way the steering wheel is turned.