Why add salt to potato water?
Salting the water in which you cook starches (pasta, rice, potato) is an effective way of enhancing the flavour of the finished product - boiling starches absorb salt well (which is why adding chunks of potato to an overall salty stew will lessen the apparent saltiness of the dish.

But salt does other things. When I am making roasted potatoes, I parboil them for 5 minutes before drying and roasting them in oil. if you divide them into two batches and boil one half in unsalted water and the other half in well salted water (1tbsp/2 quarts water), the salted potatoes will brown and crisp much better than the unsalted ones. I'm not sure why this is, but I would encourage you to try it because it's amazing to see.