Why bicycle not stop when we do reverse paddling?

In the rear gears there is a ratchet mechanism which allows the wheel to spin freely if you are rolling down a hill (or if you are pedalling backwards) but locks in place when you are pedalling and pushes the wheel around.

Sometimes when you are rolling slowly you might be able to hear the clicking noise, that's the ratchet mechanism making the noise.

For a diagrammatic representation of how it works, take a look here:

http://en.wikipedia.org/wiki/Ratchet_(device)

modern bikes are made to do that, so if your going down a hill for example, you don't have to peddle at all(if the peddles were permanently linked to the gear your the peddles would force your legs to move.