They can't replace each other, each have it specific use.
A monopod will NOT prevent camera shake. It will help the photographer to lighten the weight of the camera if the lens is a big lens.
You cannot shoot nite scene with monopod. It may not work well in low light.
Tripod is bulkier then monopod but the puspose it serve is to prevent hand shake and for those with super telephoto lens. and taking nite shot.
A tripod will definitely be better than a monopod given ideal conditions, but the fact is that there are times when we have to resort to monopods for reasons such as:
the place we're shooting at doesn't allow tripods (eg. museums)
there isn't enough space to set up a tripod (eg. in dense vegetation)
you need to be constantly on the move during the photo shoot (eg. sports photography)
and, of course, as you've mentioned, when we simply need to travel light
However, as has already been pointed out, monopods are not a replacement for tripods by any means, and should not be treated as such. In situations like night photography or long exposures, monopods will be totally inadequate. Pick your tools according to the task at hand.