Gear ratios refer to the relationship between the number of teeth on two or more gears that are in contact with each other. These ratios determine how much the driven gear will rotate for every rotation of the driving gear, and they play a crucial role in determining the speed, torque, and overall performance of mechanical systems such as bicycles, cars, and industrial machinery. By changing the gear ratios, one can adjust the efficiency and power output of these systems to suit specific needs or conditions.