According to Jack Norris, Registered Dietitian and Executive Director of Vegan Outreach, iodine is needed for healthy thyroid function which regulates metabolism. Both too little—and too much—iodine can result in abnormal thyroid metabolism. A goiter (enlarged thyroid gland) can be caused by eating both too little or too much iodine. The symptoms of either can be hypothyroidism—in which metabolism slows and weight and cholesterol increases—or hyperthyroidism—where metabolism increases resulting in weight loss.
Iodine is consistently found in only a few foods such as dairy products (iodine solutions are used to clean the cows’ teats and dairy equipment and end up in the milk) and seafood (including seaweed). In plant foods, iodine is found inconsistently and depends on the iodine content of the soil—food grown near the ocean tends to be higher in iodine.
Vegan iodine supplements can be found in most grocery or natural food stores, and most multivitamins contain iodine. The Dietary Reference Intake (DRI) for adults 19 years old and over is 150 µg. See here for Dietary Reference Intakes for various age groups and life stages. In the U.S., you can get 75 µg of iodine from 1/4 teaspoon of iodized salt.