Think of Silk damping as a consequence of heat conduction in the primordial plasma. In the initial conditions, there are temperature variations potentially down to arbitrarily small scales. However, heat spreads over time from hot regions to cold regions, and this effect washes out small-scale temperature variations. Large-scale temperature variations still persist because the heat does not have enough time to conduct across those scales.
(Silk damping is usually described as a consequence of photon diffusion, but that's just the underlying mechanism for the thermal conduction.)