Seed Expert, Earth Scientist and Organic Farmer Roy Nurmi writes:
Porosity of a soil is the volume of all the open spaces (pores) between the solid grains of soil. For growing things in soil, the porosity is important as it defines the volume of water that can be held in a given volume of the soil.
Soil permeability is the property of the soil pore system that allows fluid to flow. It is generally the pore sizes and their connectivity that determines whether a soil has high or low permeability. Water will flow easily through soil with large pores with good connectivity between them. Small pores with the same degree of connectivity would have lower permeability, because water would flow through the soil more slowly. It is possible to have zero permeability (no flow) in a high porosity soil if the pores are isolated (not connected). It is also to have zero permeability if the pores are very small, such as in clay.