Radiation refers to energetic particles that deposit their energy, often harmful, into tissue. The particles can be either:
To do significant damage, the particles must have energies in the keV or MeV range. The source of such radiation is usually either nuclear (e.g. radioactive material) or cosmic rays. When charged particles travel through tissue they damage tissue by stripping electrons from atoms and molecules, thus destroying their ability to function. Photons also interact principally with electrons, since electrons are much more easily removed from atoms than are nucleons. Neutrons always react first with a nucleus, but even with neutrons, most of the damage is caused by removing electrons from the protons released from the first nuclear interaction of the neutron.
The surface of the earth is in a constant bath of cosmic rays which leave ionization trails through all living organisms. However, biological tissue is remarkably adapt at repairing the damage. Radiation is most harmful when many molecules are destroyed in a neighborhood by concentrated radiation. Thus the damage of radiation is not linear with the amount of radiation received. This makes measurement of the harm of radiation difficult. If a worker at a power plant receives an amount of radiation equal to one-year's-worth of cosmic rays, the health effects are much more serious if the exposure was over a short time span, and more serious again if limited to a small fraction of the body.
However, even a 1 foot thick fuselage wouldn't protect you from being ripped apart on an atomic scale by fast neutrons, instead your body is a neutron "catcher" due its high water content...