According to About.com, mature rivers are bodies of water that flow over wider valleys and snake along flat plains. The meandering streams then create larger loops that develop into oxbow lakes.
When mature rivers start to curve, they erode and cut the outside of the curves. They then proceed to deposit sediment on the interior of the curves. Streams move rapidly at the outside curves and slower on the inside curves. As time goes by, the deposition and erosion continues, and the curves become more circular and larger. An example of a mature river is the Mississippi, which winds and flows into the Gulf of Mexico.