An Indian vegetarian meal almost always includes a bowl of plain curd, and it is eaten as its own element rather than spooned over other dishes. The placement is deliberate and does specific work.
It functions as the cooling counterweight
Much of the plate is built on chili, warming spices and fat. Curd is cold, sour and mild, and it interrupts the accumulation of those effects.
Capsaicin, the compound responsible for chili heat, is fat-soluble, and the fat in dairy carries it away from the receptors more effectively than water does.
That is why a spoonful of curd relieves heat while a glass of water does not, and why the bowl sits within reach through the whole meal.
It supplies protein that the rest of the plate distributes thinly
A vegetarian meal draws protein from legumes and grains spread across several dishes. Curd adds a concentrated dairy protein in a single component.
Because it is unheated and unspiced, that contribution arrives without adding to the fat or salt already present in the cooked dishes.
In many households the curd bowl is the most consistent element of the plate, present whether or not the rest of the meal changes from day to day.
The sourness has a functional role
Fermentation produces acid, and acid on the palate resets the perception of richness, which is why a sour element appears somewhere in almost every Indian meal structure.
Curd provides that acidity in a form that is also creamy, so it performs the job that a squeeze of citrus or a pickle does elsewhere on the plate.
It is eaten last for a reason
Many regional meal sequences finish with curd and rice, a deliberately plain combination that closes the meal on something mild after a series of intense dishes.
The custom is old and is usually explained in terms of digestion and settling, whatever the underlying mechanism, and it survives because the sequence eats well.
American substitutes are not equivalent
Set curd is thinner, tarter and less strained than most US supermarket yogurt, and sweetened or vanilla varieties are unusable in this role.
Plain whole-milk yogurt thinned slightly with water and left at room temperature to sharpen is the nearest practical substitute, and setting curd at home from whole milk is straightforward.