Some waterfalls are found in places where there are soft and hard layers of rock lying as flat sheets. Others were produced when glaciers cut deep trenches during the Ice Age. The waterfalls produced by flat rock layers have been drawn out for you in a side-on view here.
Usually the river flows quite slowly before it reaches the waterfall.
The top edge of a waterfall is called the lip. The part where the water drops is called the fall. At the bottom, the water, and stones it is carrying, wear out a deep pool. This is called a plunge pool.
Some of the stones and water splash back under the fall and wear away the soft rock. As the soft rock wears back, the rock making the lip is left standing clear until, one day, it cannot hold up any longer. It then breaks off.
In this way the waterfall slowly wears its channel upstream, leaving a gorge below to show where it once formed. The river often flows in a narrower channel below the waterfall.