The earth and sand deposited there are called "sediments" and they build up to form what is called a "delta"; a triangular wedge shaped like the Ancient Greek letter "D" - hence "delta".
The soil deposited at the mouth of a river is called silt.
A Delta is formed
Delta
Delta
The river runs however long, all the while picking up sediment, sand, rocks, etc. and continue doing this for the river's length, and at the very end of the river (mouth), all of this sediment is deposited, leaivng sand at the river mouth.
That is called a river 'delta'.
an alluvial fan
Well heavy earth material like sand slows down at the mouth on the river. It slows down at the mouth because at the source of the river is the fastest but as it is moving down the plain it is slowing down because of friction. Also because the eroded sand that is in the water is making the water heavier which means it will slow it down
sand bars
The abrasion and attrition combined with hydraulic action on the river bed and the river banks erode away the underlying rock which results in small grains of rock we call sand. Depending on the speed of the river and the size of the particles, the sand will be deposited by the river at different stages (usually though it is found near the mouth of the river).
Larger particles are deposited first as a stream loses velocity. Gravel would be deposited first, since it is the largest (out of Clay, Silt, Sand, and Gravel)
Moraine.