Storing boiled potatoes in the refrigerator increases their content of resistant starch (from 3.3% up to 5.2%), making them slower to break down in your intestines, and also lowering the amount of insulin your body produces after eating them.
A study by Swedish researcher Margaretta Leeman published in 2005 has shown that storing cooked potatoes for 24 hours at 8 degrees Celsius prior to eating them reduces their insulinaemic index or the amount of insulin produced in response to eating them by 28%. This is good news for women with PCOS who are often told simply to completely avoid eating potatoes due to their high glycaemic and insulinaemic indices. This means that a small serve of potato salad prepared the day before and stored in the refrigerator could be permitted.
Leeman M, Ostman E, Björck I. Vinegar dressing and cold storage of potatoes lowers postprandial glycaemic and insulinaemic responses in healthy subjects. Eur J Clin Nutr. 2005 Nov;59(11):1266-71.