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GEARS are mechanical devices that alter the speed and (sometimes) the direction of motion of rotating objects. They scale the torque (turning force or moment of force). Gears are ubiquitous being found in cars, trucks, bicycles, industrial equipment and in fact almost anywhere that turning forces have to be managed in some way. The gearbox of a car is probably the best known example.
GEAR RATIOS: the gear ratio is a measure of the comparative speeds of the gear wheels. In this animation, the little wheel makes exactly two turns for every one turn of the larger wheel, so the gear ratio is 2:1. The little triangular pointers towards the edges of the gear wheels (green on the smaller wheel and red on the larger wheel) let you follow and compare the rotations of the two cog wheels. Notice how the two cog wheels rotate in opposite directions. This is how gears can reverse the direction of rotation of a motor, for example.