Dishes that benefit from one or two days storage are characterized by the fact that they are thick (viscous), contain some fat and/or are spicy or herby. Often these foods are actually emulsions or dispersions of fat in an aqueous phase, stabilized by proteins, starches or even food particles. Examples: lentil dishes such as dahl, pea soup, fish soup, lamb stew, shrimp sauce, mayonnaise etc.
I believe the taste development has nothing to do with enzymatic reactions, as these will be suppressed in the refrigerator, but more with the redistribution of aromatic compounds and other taste enhancers over the food. In potato loving countries, it is a well known kitchen secret to add some potato to a simmering stew when the cook inadvertently added too much salt. The salt is preferentially absorbed by the potato and removing the boiled potato reduces the salty taste. A spicy dish when freshly made can sometimes taste sharp, but may mellow into a delicious aromatic dish after one or two days storage. Re-distribution of aromatic compounds may be a continuous process and may take more time in viscous emulsions and dispersions (i.e. the thick soups, stews and sauces). Keeping this in mind may help the cook to create excellent tasting soups, stews and sauces.
Table 1. Time to reach optimum taste for various foods and drinks.