How could the rerouting of a river affect the surrounding lowland?

A river's meandering course may sometimes be rerouted into a straighter, man-made channel. This may be done if it is cost effective (in the long term), a benefit (flood control, speed up water flow, allow original course to be developed for building, etc). This happened to a short stretch of the River Dee, UK, the original route can still be traced with a careful study of the surrounding land.