Waterfalls are naturally occurring river formations involving all or a portion of the flowing water falling vertically. The can be visually stunning and are frequently popular tourist attractions. The waterfall you see above is Price's Falls in the Arbuckle Mountains in Oklahoma.
The movement of the water erodes the rock over which it flows and slowly erodes it. Over time this process will slowly move the falls farther and farther back into the rock.
Another type of waterfall is demonstrates the opposite process. Through the process of precipitation, minerals are deposited from the water onto the rocks. This can be seen here in Oklahoma at Turner Falls where the rock tufa can be easily spotted around the falls.
Another example is Sitting Bulls Falls in New Mexico which you can see in the video to the left. Due to the continuously deposited calcium carbonate, the rocks of the falls grow outward.