Permeability is a property of foundry sand with respect to how well the sand can vent, i.e. how well gases pass through the sand.And in other words, permeability is the property by which we can know the ability of material to transmit fluid/gases. The permeability is commonly tested to see if it is correct for the casting

Casting

In metalworking, casting involves pouring liquid metal into a mold, which contains a hollow cavity of the desired shape, and then allowing it to cool and solidify. The solidified part is also known as a casting, which is ejected or broken out of the mold to complete the process...

 conditions.
The grain size, shape and distribution of the foundry sand, the type and quantity of bonding materials, the density to which the sand is rammed, and the percentage of moisture used for tempering the sand are important factors in regulating the degree of permeability.
An increase in permeability usually indicates a more open structure in the rammed sand, and if the increase continues, it will lead to penetration-type defects and rough castings.