In principle, it is simply a description of the repulsion of ions of the same charge as the ion exchanger itself. The consequence is an exclusion of these ions from the pores of the packing that depends on the total ionic concentration in the mobile phase.
Case 1: let us run a mobile phase with a very low salt concentration, say 1 mM NaCl, on a packing with an anion-exchange capacity of 1 meq/mL. This means that the concentration of fixed ions in the pores is about 1000 times larger than the concentration of ions in the mobile phase. Let us now inject another salt, let's say KBr. The K+ ions will freely penetrate into the pores, and if they do not interact any stronger with the ion-exchange sites than the Na+ ions, they will elute unretained. The Br- ions however have a problem: the concentration of ions of the same charge in the pores is high due to the very high concentration of the fixed ions on the ion exchanger. The concentration of fixed anions in the pores is about 1000 fold higher than the concentration of anions in the mobile phase. Thus the analyte anions are repulsed by the fixed anions of the ion exchanger Thus they are rejected from the pores and must elute at an elution volume close to the interstitial fraction of the column. Bottom line: injecting KBr, I get two separate peaks: one for the Br- ion, which elutes early, and one for the K+ ion, which elutes later.
Case 2: I increase the ion concentration in the mobile phase to 1M NaCl. Now, the pores are full of ions, and the few additional ions on the surface of the packing do not make a lot of difference. Now, there is not much of a reason left for the Br- ion to stay out of the pores, and it will elute close to the true void volume, where the K+ ion is eluting also.
And there are many cases in between, with a partial exclusion of the ion of the same charge as the surface, and the mathematical detail is the Donnan potential.
(Freely adapted from a PhD thesis by Wolfgang Werner from 1976)