Why must potato salad be placed in the refrigerator before serving?
Refrigerating accomplishes several things:


It is the right temperature to get the intended flavor.  Flavors change with temperature, and some dishes get the correct taste when cold.
Flavors get to blend more.  Aromatic spices sometimes take time to soak into the sauce, and liquids absorb into the potatoes more
Cold is an easy way to prevent spoilage.  Potato salad usually contains mayonnaise, which is a natural growth medium for bacteria.  By cooling the salad you can leave it out to serve for a couple hours without risking illness.


Food safety of Potato Salad:
For potato salad, you have about 2 hours of safe eating in the 40-140F temperature range. Refrigerating is an easy way to extend this, by cooling below 40F. For hot salads, you can either reheat before serving, or keep it hotter than 140F by using a chafing dish and can of Sterno.

About Mayonnaise in Potato Salad:
Commercial mayonnaise is too acidic to spoil easily, but when mixed in with potato salad it can be diluted enough to spoil.  It is better to refrigerate than take the risk, right?  If you use homemade mayonnaise, you run the risk of salmonella on top of this.