Radiation is given off by radioactive material. Keep the material off your body, and you are usually ok. The trouble is that even small quantities can be very deadly if swallowed or breathed, and any material in dust or liquid can be very hard to get off the skin. A decon scrub can be a very painful experience, and you may still be hot. Of course, extremely strong radiation can penetrate several feet of space (or even heavy shielding), just like x rays, but any radioactive material is dangerous in tiny quantities if it is ingested so the radiation is in actual contact with tissue. TB is right, the suits don't protect you from the radiation, but from getting the radiating matter on you in the first place.

In general, there are three types of radiation,alpha, beta, and gamma, of increasing power. The first two can be easily shielded against, by skin and paper, respectively, although an alpha or beta emitter can be dangerous in contact with your body or if ingested. Gamma rays are highly penetrating, only distance or heavy shielding can stop them.

To make things more complicated, the effects of radiation are cumulative, they may not manifest themselves until years later, and they are statistical(any effect at any dosage is noticeable in only a portion of the population, that is, there is no "level" of danger, or safety, just better or worse odds. The effect depends on proximity, type, duration, and intensity, and repetition. To make things worse, we can detect accurately levels millions of times lower than the lethal level, so it is hard to tell people when they are safe or not.

There is no safe level, but that statement is also misleading. Even brief exposure can cause cancer to a tiny portion of the exposed, just like one sunburn or one cigarette might cause cancer in a tiny portion of the population. A "lethal" dosage is defined as one that kills half the population exposed to it. And some materials are extremely toxic even in microgram quantities (particularly Plutonium) not because they give off a lot of radiation, but because the dust in your lungs will eventually cause cancer from prolonged exposure.

Pretty much all the press statements you hear about radiation effects are misleading, not because the press lies, but because the science is so complicated and reporters are science challenged. A given dosage of so many rads, or rems (or some other unit) may be dangerous under some circumstances but safe in others. and of course, there are low levels of radiation in the environment from natural sources that we've dealt with since the beginning of time. Another problem is that very dangerous exposures can be absorbed without the victim feeling any immediate symptoms. Some may not turn up for years. In my opinion, those guys in Japan who received skin burns after only a few minutes exposure are dead men walking.

There is an entire branch of toxicology, health physics, devoted to assessing the effects of radiation, and it is by no means an exact science. Safety standards for dosages are usually decided by committee, and are being revised up or down all the time. Many are debated by "industry reps" for "economic reasons". Toxicologists determine the lethality of a material by graphing the percentage of a test population (or historical sample) as a function of exposure, and extrapolating the curve into smaller numbers. After a while, it becomes very difficult to determine what that curve looks like for the outliers. For example, if 50% of the rats die at X exposure, and 25% of the rats die at X/2 exposure, how many rats will die at at X/1000 exposure? 1/2000 of them? It's a reasonable guess, but it's still a guess.