The following text presents some introductory concepts of radiation and exposure. This topic is complex and links are provided for additional reading.
In the last couple of months I have been reading about effects of radiation on the human body. This renewed interest came after the April anniversary of the Chernobyl Disaster during which the firefighters and plant workers that responded to the accident received a lethal dose of radiation. Those workers and firefighters developed what is called Acute Radiation Syndrome (ARS) or radiation sickness. Furthermore, I have learned that high radiation exposure can occur not only in nuclear power plants, but in nuclear waste reprocessing plants, research institutions, hospitals, and facilities specializing in food irradiation.
Radiation & Dose Basics
Radiation is energy released by atoms undergoing decay. This energy can be converted to heat, as in nuclear reactors, and in biological tissues this energy can cause ionizations. The ionizing radiation can be in the form of alpha, beta, gamma, electrons. 
Amount of such radiation is characterized by a dose. The commonly used SI unit is Gray (Gy) with units J/kg . Gray describes how much energy has been absorbed per unit of mass. For example, an 80 kg person that received a dose of 10 Gy had absorbed 800 Joules of energy from particles (alpha, beta, gamma, etc.) that have hit the tissue.
Effects on Body
Radiation has a destructive effect on the body; whereas some amount is tolerable, certain amounts are lethal. Acute Radiation Syndrome (ARS) occurs when body is exposed to large radiation doses within a short period of time. The amount of time is critical, for example nuclear plant workers receive small doses over years, which might not be tolerable if received all at once in a matter of seconds. The dose we are talking about is at least 0.5 Gy to produce mild symptoms and with 3.5+ Gy causing severe symptoms with LD50/30 (50 % of those exposed will die within 30 days if left untreated).
For a detailed discussion on physiologic effects look at a June 2004 article from Annals of Internal Medicine titled Medical Management of the Acute Radiation Syndrome 
Effects on Body
The following video shows soldiers on the roof of the containment building of the Chernobyl NPP. These people are using shovels to clean up radioactive graphite following the explosion. All of these people received lethal doses of radiation.