Why do some foods taste better the next day?

For pastas at least, the noodles have a chance to absorb more flavor directly into the bland noodles. Same with potatoes in stews.

If the dish cools and is then reheated, more water is lost into the air. This effectively reduces the dish and intensifies flavors.

In the Good Eats episode "Stew Romance", Alton Brown says

See, as gelatin cools, it moves from a suspended colloidal state to a gel state, which if concentrated, can be quite strong. [...] And that is why our meat gets pretty hard when it cools down. Now, what’s really interesting, though, is that once gelatin has reached the gel state, it takes more heat to re-dissolve it than it did to render it from collagen in the first place. [...] Ahh, the meat is perfectly heated through, but it’s not falling apart. That’s because we let it cool down before reheating, and that is why stews, braises, fricassees, and blanquettes are always better the second day.

_{(Note that, as usual for Alton, his science is sound, but his other "facts" are to be taken with a huge grain of salt. For instance, the dish he makes that he calls Hungarian Goulash isn't Hungarian and isn't goulash. And the actual Hungarian stew that most Americans think is goulash is pörkölt. I haven't the foggiest idea where he got "pörkoft" from. Oh, and potatoes are very much a standard part of goulash, that's part of what distinguishes goulash from pörkölt.)}

In any case where the flavours are water soluble, and the main ingredients soak up water, this will happen. This is especially true for soups, stews and lentil dishes. It holds equally though for anything cooked in water.

I noticed it particularly in my lentil dahls. In the vening, when it's just come off the fire, the water seems a little grainy, and the dish doesn't have the right flavour. The next morning, the spices have dissolved better, and the water/spice solution has soaked into the lentils.

During cooking we have the active chemical processes occurring. However, much like any other chemical process, the decay of the compound created is just as metamorphic.

Heat excites the passive transport processes but also cauterizes food making it useless after a certain point for flavor infusion. The cooling and re-pressurizing undergone in the refrigerator will cause flavors to continue redistributing themselves without further cooking the food (duh) and cause the fat and water layers to redistribute themselves only to be reincorporated during the re-heating process.

Passive transport means moving biochemicals and atomic or molecular substances across the cell membrane. Unlike active transport, this process does not involve chemical energy. The four main kinds of passive transport are diffusion, facilitated diffusion, filtration and osmosis.

For soups, stocks, sauces, chilis, or any preparation/recipe that tends to have a lot of loose fat, refrigerating it for several hours will cause the fat to congeal at the top, at which point it is easily skimmed off. That will definitely give it a less greasy texture and flavour.

I'm not sure if that's the kind of answer you were looking for, but since you did explicitly mention stews, soups, and sauces, this is likely to apply. I think many people skim the fat off without consciously knowing what they're doing (I always used to do it before I really understood what was going on), and as a result, the reheated food has a heartier flavour.

I heard a theory from a professional chef that it is a concept similar to the tempering of chocolate which has to be alternately heated and cooled to exact temperatures to come out right.

Also, a little alcohol can release flavours you get from non water soluble compounds.

My personal theory is that as I cook a dish, I get habituated/desensitized to the aromas through extended exposure. The next day, I'm experiencing all those intense aromas and flavors fresh, and so they feel much intense, and I enjoy the dish more.

Have you ever cooked a dish with a strong aroma, say a tomato sauce? The aroma of onions, garlic, tomatoes, etc. will fill the kitchen and maybe even the whole house. Say you leave it simmering on the stove while you go outside for 10 minutes... when you come back in, the aromas will feel incredibly intense as you have let your smell receptors relax and partially restore their supplies of neurotransmitters.