Several different theories have been proposed to explain the formation of Liesegang rings.  The chemist Wilhelm Ostwald in 1897 proposed a theory based on the idea that a precipitate is not formed immediately upon the concentration of the ions exceeding a solubility product, but a region of supersaturation occurs first.  When the limit of stability of the supersaturation is reached, the precipitate forms, and a clear region forms ahead of the diffusion front because the precipitate that is below the solubility limit diffuses into the precipitate. This was argued to be a critically flawed theory when it was shown that seeding the gel with a colloidal dispersion of the precipitate (which would arguably prevent any significant region of supersaturation) did not prevent the formation of the rings.
Another theory focuses on the adsorption of one or the other of the precipitating ions onto the colloidal particles of the precipitate which forms.  If the particles are small, the absorption is large, diffusion is "hindered" and this somehow results in the formation of the rings.
Still another proposal, the "coagulation theory" states that the precipitate first forms as a fine colloidal dispersion, which then undergoes coagulation by an excess of the diffusing electrolyte and this somehow results in the formation of the rings.
Some more recent theories invoke an auto-catalytic step in the reaction that results in the formation of the precipitate.  This would seem to contradict the notion that auto-catalytic reactions are, actually, quite rare in nature.
The solution of the diffusion equation with proper boundary conditions, and a set of good assumptions on supersaturation, adsorption, auto-catalysis, and coagulation alone, or in some combination,  has not been done yet, it appears, at least in a way that makes a quantitative comparison with experiment possible. However, a theoretical approach for the Matalon-Packter law predicting the position of the precipitate bands when the experiments are performed in a test tube, has been provided 
A general theory based on Ostwald's 1897 theory has recently been proposed.  It can account for several important features sometimes seen, such as revert and helical banding.