From what I gather, it's technically Potassium Iodide, (KI) rather than elemental Iodine that is prescribed for radiation exposure.

The CDC's page on this goes into more detail.

Basically, it can only protect the Thyroid from injury due to radioactive Iodine. It's ineffective when there is no radioactive Iodine and doesn't protect other organs.

The way it works is by supplying enough non-radioactive Iodine to your Thyroid that it can't absorb any of the radioactive Iodine that you are exposed to.