A pothole is formed when a circular current of water carrying small pebbles and sediment begins to wear away a rock surface. The force of water and the sediment it carries is greater than the resistance of the rock. Once the process has begun, it continues and the rock in that location continues to erode away.
As these depressions deepen, pebbles can become trapped in them. As a result of the eddie currents, the pebbles drill into the depressions making them more circular, wider & deeper. Pebbles will only be able to erode a river’s bed though if the rock the pebble’s made of is stronger than the rock the river bed is made of.