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I have encountered a type of unit that I cannot understand. The unit describes the rate of permeation through a substance:(cm^3 . mm)/m^2 . d . atm

Could someone please explain how to interpret these units? Please attempt to leave the answer in simple - to - understand terms as chemistry, not engineering, is my primary field.

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$$ \frac{\left(\mbox{amount of gas}\right)\left(\mbox{thickness of membrane}\right)} {\left(\mbox{membrane area}\right)\left(\mbox{time}\right)\left(\mbox{differential pressure of gas}\right)} $$

Units of gas permeability constants (source of the formula)
Gas Barrier Introduction
Introduction to Material Permeability Indexes

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