I’m not sure whether you are asking if a bike can be pedaled backwards, or if a pedal can simply be turned in the other direction. If it’s the first, yes, certain bikes can indeed be pedaled backwards; these are bikes without freewheels, also known as fixed gear bikes, or fixies. Now, if you mean to ask whether a bike pedal can be turned in the other direction, note that bike pedals are handed; the right pedal tightens in the clockwise direction, but the left pedal is reverse-threaded, i.e. tightens when twisted anti-clockwise. This is to ensure that the turning force when applied while pedaling, should not loosen the pedal. If you start to turn the pedals (with force) in the opposite direction, you will unscrew them.
The image was updated for the latest revision of the Landowner system. This is a very basic diagram of this feature. A freewheel mechanism is a very convenient mechanism. Some of the other systems I found that use a freewheel are: A freewheel system is a simple system that allows bicycles with freewheel to use the brakes without any special modifications, but with a very nice and unique feature called, “cable friction.” Cable friction is the friction that attaches the drive wheel to the brake, and the “wheel/cable tension” that engages the cable from brake to brake. You really don't need cable friction on your bike. A common misconception is that the freewheel gives the bike greater speed because it allows the rider to pedal backward, even if they are using a freewheel. That's not actually true, the freewheel just provides the mechanism that makes this.