Opacity (or Attenuation Coefficient) is a measure of opaqueness of a material, i.e., to what degree light is absorbed as it passes through. As used in astrophysics, the term specifically means the rate at which the density of a material reduces the Intensity of a beam of light passing through. It varies by Wavelength.
Opacity can occur at values from 0 to ∞. It decreases the intensity as follows (given uniform opacity and density):
Id = I0e-κρd
The opacity and intensity in this equation can be subscripted by ν to specify the intended wavelength.
Since the opacity varies by wavelength, some assumption regarding the spectrum must be made to define an opacity applicable to more than a single wavelength. The Rosseland Mean Opacity is an example.
Absorption Coefficient means roughly the same thing as opacity, but generally it is used to include the effects of the material's density, whereas opacity is such an Absorption coefficient divided by density, thus including only any non-linear effects of the density.