Leonardo Davinci invented the chain drive in the 15th century. It allows the torque created in the pedal to be directly applied to the rear wheel to power the bike. the chain drie was not added to the bike until the invention of the safety bike in the late 18th century. Shortly after the the addition of the chain drive gears were added to the bike to make them even more efficient. Gears work as a force multiplier between the pedals and the wheels. They are used to change the ratio of number of times the wheel turns to number of pedals.
http://www.exploratorium.edu/cycling/gears1.html
In the above animation you can see that for every one time you pedal the wheel turns twice, so as you enlarge the front cog and/or decrease the size of the front cog the ratio goes up. This is advantageous as it does not limit your speed to the speed you can pedal. on the other hand if you are traveling you want to decrease the size of the front cog while increasing the size of the rear cog which will allow you to use less power.