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Why doesn't a bicycle move backwards when one pedals back?
Figure 01. Pawl and leaf spring system. Figure 02. Ratchet There is a tick sound every time you push the pedal. It is the freewheel mechanism of the rear wheel comprising of two components- the ratchet and the pawl. When you pedal, the pawls lock themselves to the dents in the ratchet part thus forcing the inner mechanism to rotate. The pawls are held in upward position by using tiny springs (you can see them under the pawls as leaf like structures - leaf springs). When you pedal backwards or when you stop pedaling the springs holding the pawls upright, collapse and the pawls fall back in their collapsed positions. Thus making the freewheel free. However, bicycles like fixies and BMX have mechanisms which allow us the pedal in reverse also. This is the simplest explanation. Please note that expensive hubs and axles use more complex mechanisms. But the basics remain the same. Note. The images were borrowed from the internet.
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Rotate PDF: All You Need to Know
The pictures were not used without permission, the credit for the pictures and captions is given here.