The Einstein-Smoluchowski Relation connects the diffusion coefficient of a particle in a fluid with its mobility through the equation D = μkT, where D is the diffusion coefficient, μ is the particle's mobility, k is the Boltzmann constant, and T is the absolute temperature. This relation is fundamental in statistical mechanics as it provides a link between microscopic particle behavior and macroscopic observable quantities, highlighting the thermal fluctuation influences on diffusion processes.