Iodine is an essential trace mineral. It's required for the formation of activated thyroid hormones T3 and T4. The amount of thyroid hormones in circulation, and the body's sensitivity to them, strongly influences metabolic rate. Iodine deficiency can lead to weight gain and low energy. In more severe cases, it can produce goiter, an enlargement of the thyroid gland.
Iodine deficiency is also the most common cause of preventable mental retardation worldwide. Iodine is required for the development of the nervous system, and also concentrates in a number of other tissues including the eyes, the salivary glands and the mammary glands.
There's a trend in the alternative health community to use unrefined sea salt rather than refined iodized salt. Personally, I use unrefined sea salt on principle, although I'm not convinced refined iodized salt is a problem. But the switch removes the main source of iodine in most peoples' diets, creating the potential for deficiency in some areas. Most notably, the soil in the midwestern United States is poor in iodine and deficiency was common before the introduction of iodized salt.
The natural solution? Sea vegetables. They're rich in iodine, other trace minerals, and flavor. I like to add a 2-inch strip of kombu to my beans. Kombu is a type of kelp. It adds minerals, and is commonly thought to speed the cooking and improve the digestion of beans and grains.
Dulse is a type of sea vegetable that's traditionally North American. It has a salty, savory flavor and a delicate texture. It's great in soups or by itself as a snack.
And then there's wakame, which is delicious in miso soup. Iodine is volatile so freshness matters. Store sea vegetables in a sealed container. It may be possible to overdo iodine, so it's best to eat sea vegetables regularly but in moderation like the Japanese.
Seafood such as fish and shellfish are rich in iodine, especially if fish heads are used to make soup stock. Dairy is a decent source in areas that have sufficient iodine in the soil.
Cod liver oil is another good source of iodine, or at least it was before the advent of modern refining techniques. I don't know if refined cod liver oil contains iodine. I suspect that fermented cod liver oil is still a good source of iodine because it isn't refined.