Alluvium is laid down when a river floods over its banks. The material it is carrying then settles out and creates a layer. This layer is often silty or muddy and this is why people use the words silt or mud instead of alluvium. However, it may also contain sand and even pebbles.
Alluvium is the material which builds up to make the flat land either side of a river that is called a flood plain.
You can see the thickness of alluvium by looking at the banks of a river.
The picture above shows you that a great many sizes of material that can be called alluvium are carried by a river. The smallest pieces that you can see individually here are sand. The fine material around the sand is silt and mud.
The video below shows you sand that is also one of the materials in alluvium. We can see it at times of low flow when part of the river bed is exposed.