When was the gears invented?

In the 3rd century B.C., various Greek Inventors used gears in water wheels and clocks, and sketches of various types of gears of around this time were found in Leonardo da Vinci's notebooks later on.

How does the gear work?

Each time you pass power from one gear wheel to another, you can do one of three things:

•Increase speed: If you connect two gears together and the first one has more teeth than the second one (generally that means it's a bigger-sized wheel), the second one has to turn round much faster to keep up. So this arrangement means the second wheel turns faster than the first one but with less force. Looking at our diagram on the right (top), turning the red wheel (with 24 teeth) would make the blue wheel (with 12 teeth) go twice as fast but with half as much force.

•Increase force: If the second wheel in a pair of gears has more teeth than the first one (that is, if it's a larger wheel), it turns slower than the first one but with more force. (Turn the blue wheel and the red wheel goes slower but has more force.)

•Change direction: When two gears mesh together, the second one always turns in the opposite direction. So if the first one turns clockwise, the second one must turn counterclockwise. You can also use specially shaped gears to make the power of a machine turn through an angle. In a car, for example, the differential (a gearbox in the middle of the rear axle of a rear-wheel drive car) uses a cone-shaped bevel gear to turn the driveshaft's power through 90 degrees and turn the back wheels.

What's the catch?

You might think gears are brilliantly helpful, but there's a catch. If a gear gives you more force, it must give you less speed at the same time. If it gives you more speed, it has to give you less force. That's why, when you're going up hill in a low gear, you have to pedal much faster to go the same distance. When you're going along the straight, gears give you more speed but they reduce the force you're producing with the pedals in the same proportion. 

Whenever you gain something from a gear you must lose something else at the same time to make up for it.

Source http://www.explainthatstuff.com/gears.html