An absorption coefficient is a measure of how much electromagnetic radiation (EMR) (e.g., light) is absorbed by a substance as the EMR passes through it. It is used in modeling the effect of gas on the EMR passing through, such as radiative transfer equations. The coefficient is a ratio of the EMR absorbed over a unit length of the substance, to the EMR before the absorption. Its value depends upon the substance and its density and can depend upon temperature and can vary over the course of the EMR's travel through the substance.
The term a scattering coefficient is used for an analogous ratio indicating how much of the EMR will be scattered rather than pass through. Attenuation coefficient indicates the combined effect of both (but the phrase absorption coefficient may be used to mean this.) An emission coefficient is an analogous measure the amount of additional EMR as the EMR is passing through a substance.
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 is another measure of absorption of a substance, consisting of the absorption coefficient per unit mass, i.e., the absorption coefficient divided by the substance's density.
Note the term absorption coefficient is sometimes used with another (related) meaning: as a synonym for opacity as defined on this site. The difference is whether the value includes the material's density as a factor or not, so you have to note the two possibilities in references to an absorption coefficient.