Linked from
The 12 pages that link to Diffusion coefficient, each with the reason it gives.
DiffusionRelated: It sets the rate connecting a concentration gradient to diffusive flux.
Molecular diffusionRelated: Its value sets the rate at which a concentration gradient smooths out.
Vacancy defectRelated: Vacancy-mediated jumps contribute to atomic diffusion coefficients.
Itô's lemmaRelated: Its square multiplies the second derivative in the one-dimensional formula.
Nernst–Planck equationRelated: It sets the strength of concentration-driven flux.