Pebbles are small stones, worn smooth by erosion. A pebble can be an igneous, sedimentary or metamorphic rock. Any kind of rock can become a pebble, as long as they go through a process of erosion. In particular, river pebbles are formed by an erosional process called "SALTATION", which is due to the alluvial transport of rocks by rivers.  That's where a rock is picked up and carried for a short distance, dropped, picked up and carried again, dropped again, and so on.  Every time the rock is dropped pieces of the corners may break off until all the corners are gone and the pebbles is as smooth and round as it can get.