Certain dishes are noticeably better on the second day, and it is not imagination or lowered expectations. Several distinct processes continue after the pan has left the heat.
Fat keeps dissolving aromatic compounds
Many spice and aromatic compounds dissolve in fat rather than water, and that dissolution continues slowly for hours after cooking stops.
Over a night in the refrigerator, more of those compounds move out of solid particles and into the fat, from where they distribute through the dish.
This is why a curry tastes more even and less like separate ingredients the next day, since the fat has finished carrying flavour into every part of it.
Starch and protein continue to release material
Starch granules swollen during cooking keep leaching soluble starch into the surrounding liquid as the dish stands, which thickens it further.
Proteins that were broken down during cooking continue to release savoury amino acids slowly, adding depth that was not present when it was served.
The result is a dish that is both thicker and more savoury without anything having been added or cooked further.
Harsh compounds break down over time
Some aromatic compounds, particularly in onion, garlic and raw spices, are sharp when fresh and degrade into milder derivatives as they stand.
That degradation smooths the overall flavour, which is why a dish that tasted slightly aggressive on the day can taste rounded the next.
It also means the same process eventually goes too far, and a dish held for several days loses definition rather than gaining it.
Not every dish behaves this way
Dishes built on fresh, volatile aromatics such as herbs, citrus and lightly cooked vegetables lose their character quickly, since the compounds involved simply evaporate or oxidise.
Anything crisp collapses as moisture redistributes, and delicate textures such as set custards and fresh cheeses do not benefit from time at all.
The dishes that improve are almost always the slow-cooked, fat-carrying, robustly spiced ones, which is a useful filter when planning what to cook ahead.
Storage conditions decide whether any of this helps
These changes only count as improvement if the food is cooled quickly and held cold, since the same time at room temperature allows bacterial growth instead.
Cooling in a shallow container rather than a deep pot moves the food through the risky temperature range far faster.
Reheating thoroughly rather than to merely warm is the other half of it, and dishes intended to be kept should be planned for that from the start.