An Absorption Coefficient is a measure of how much Electromagnetic Radiation (EMR) (e.g., Light) a substance absorbs as it passes through the substance, used in modeling the effect of gas on the EMR passing through. It is a ratio of the EMR absorbed to that entering the substance over a standard length through the substance. Its value depends upon the substance and its density. In some cases, it is specific to the direction the EMR is passing through or from a specific source, e.g., within the substance.
Similarly, a Scattering Coefficient gives such a ratio indicating how much of the EMR will be scattered rather than pass through, and an Attenuation Coefficient indicates the combined affect of both. An Absorption coefficient is the inverse of an Emission Coefficient.
An Absorption Cross Section characterizes the same measure as the Absorption Coefficient, but for a single absorbing Particle. They are related by:
σ = α / N
Opacity means roughly the same thing as absorption coefficient, but is generally used to mean the absorption coefficient divided by density, thus including only any non-linear effects of the density.