A layer of permeable rock that allows water to flow through
Is called

It is called an aquifer.

Explanation:

An aquifer also known as the confined bed is the unconsolidated sediment or rock body bearing rock readily and transmits water to wells and springs.

It has enough permeability to allow water to flow through it with relative ease.

When water enters an aquifer, it moves slowly toward lower lying places which is been discharged through springs, seeps into streams, or is held from the ground by wells. Groundwater that are in aquifers between layers of poorly permeable rock, including clay or shale, may be confined.