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Iodine tablets are a way to minimize the public health impact of radioactive releases resulting from severe nuclear accidents, such as core meltdowns. They usually contain 130 mg of potassium iodide (KI), equivalent to 100 mg of iodine. The tablets are distributed to pharmacies, schools and other public institutions near nuclear reactors. In the event of a radioactive release, the tablets are taken by people living in the affected area. The large dose of iodide temporarily saturates the thyroid gland, reducing its absorption of radioactive iodine-131 from food and air. 
Iodine-131 is a fission product with a half-life of 8 days, which can be released from a reactor when its containment structure is breached. It is preferentially absorbed by the thyroid, with large doses causing thyroid cancer. Although thyroid cancer is treatable and rarely fatal, it is nonetheless a significant public health burden in populations which were once exposed to large concentrations of iodine-131, such as in the Chernobyl area.
Iodine tablets do not act as a generic countermeasure against radiation exposure. They are only effective as a means to reduce exposure to iodine-131. Taking them more than 90 days after an accident has no effect, since iodine-131 will have almost completely decayed by then. They do not protect against external X-ray, gamma or beta irradiation or the ingestion of radioactive substances other than isotopes of iodine. This misconception found its way into an episode of House M.D.
Iodized salt does not contain sufficient quantities of iodine to act as a substitute for iodine tablets. Consuming large quantities of it will do far more harm than good, and may be fatal. This misconception led to a run on iodized salt in China after the Fukushima disaster.