Most bikes with multiple speeds contain a front and rear set of gears connected by a chain. The shift levers on your handlebars pull or release a cable that runs down the bike's tubing to the derailleur, which moves the chain from one gear to another. One shifter is for the derailleur on the rear set of gears, called sprockets; the other is for the derailleur on the gears by the pedals, called chainwheels. The bike's speeds depend on the size of the gears, the number of teeth and other factors.
Chainwheels
A bike pedal is fixed onto a lever called a crank, which does not change size. The gears next to the pedal, or chainwheels, affect the bike's leverage and resultant ease or difficulty of pedaling. When the chain is resting on a smaller chainwheel, the rider is pushing against less chain, which makes it easier to pedal. Bikes have different numbers of chainwheels beside the pedal, which permit them to have more gears.
Sprockets
When the chain is on a larger rear gear, or sprocket, the bike is in an easier, lower gear. Larger sprockets provide greater leverage, which makes pedaling easier. Bikes have different number of sprockets on the back wheel, which provide various numbers of gears. The total number of gears available is equal to the number of sprockets times the number of chainwheels. For example, a bike with seven sprockets and three chainwheels has 21 gears.
Gears
The lowest gear -- first gear -- uses the smallest chainwheel and the largest sprocket. This is the easiest gear in which to pedal, but each pedal stroke only propels you a little, which makes it hard to travel quickly. Low gears are good for climbing hills or traversing rough terrain.
The highest gear uses the biggest chainwheel and the smallest sprocket. In high gear, the bike moves further for every pedal stroke, making it easy to move quickly, but the pedals are more difficult to push, since you're pushing against more chain. High gears are good for straightaways or downhill stretches of road.
Ratios
Each gear contains a number of teeth proportional to its size. The ratio of the number of teeth on the front and rear gears determines how fast the cyclist has to pedal. A one-to-one ratio, which is when the rear wheel turns once for every rotation of the pedals, results from the front and rear gears having the same number of teeth. If the front gear has three times the number of teeth as the rear gear, then the wheel turns three times for each pedal rotation.
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