"Radiated" means that you have a measurable amount of radiation damage. Radiation still lingers in the form of fallout (note the lower-case version of this noun, as compared to Fallout - an important difference) and other hot spots. It has been rumored that there are creatures that have been exposed to such a large amount of radiation that they can actually cause radiation damage by contact. Avoid them if you can. Radiation can have several bad effects, but in general, the more radiation damage you have accumulated, the worse the effect will be. You can tell the exact amount of radiation you have been exposed to by using a Geiger counter. You can get treatment for radiation in the Vault Emergency Medical Lab, located near the entrance. It is possible that other locations may be able to repair radiation damage.