At low levels of exposure, the body's natural repair mechanisms seem to be adequate to repair radiation damage to cells soon after it occurs. It is also the dose rate which arises from natural background levels in several places. Above this, severity of illness increases with dose. Many exist in nature, the majority are created in nuclear reactions. Radon gas given out by many volcanic rocks and uranium ore has decay products that are alpha-emitters, which is why radon can be dangerous.
Beta particles are fast-moving electrons emitted by many radioactive elements.
They are more penetrating than alpha particles, but easily shielded. They are very penetrating and require shielding. Radiation dose badges are worn by workers in exposed situations to detect them and hence monitor exposure. All of us receive about 0.5 - 1 mSv per year of gamma radiation from cosmic rays and from rocks, and in some places, much more. Fast neutrons can be very destructive to human tissue.