External exposure to radioactivity can be bad, but it's far worse to have ingested a radioactive isotope, since the energy from its decay is pretty much guaranteed to damage a cell. Unfortunately, our own bodies work against us when it comes to specific isotopes, since they are either identical or closely related to the elements our bodies rely on to perform basic functions.
One example is potassium, which our body uses to maintain salt balances in cells and transmit electrical signals. In general, your body tries to hang on to all the potassium it gets, but the same mechanisms that hold onto potassium also work to keep cesium in the body, and a radioactive form of cesium has been released at Fukushima.