Radiation harms living cells.
Alpha, beta and gamma radiation enters living cells and collide with molecules.
These collisions cause ionisation which damages and destroys the molecules.
Lower doses cause less damage without killing the cell.
This can sometimes allow mutant cells to divide uncontrollably.
This is cancer.
Higher doses of radiation tend to kill cells which cause radiation sickness.
The extent of how harmful the doseage is depends on two things:
How much expose you have to radiation.
The energy amd penetration of the radiation (some types are more hazardous than others)
Outside the body, beta and gamma sources are the most dangerous.
Beta and gamma can get inside to the delicate organs where as alpha is the least dangerous as it cannot penetrate the skin.
Inside the body, alpha sources are most dangerous. Whereas beta and gamma rays are less dangerous inside the body as they can pass out without doing much damage due to their high peneration power. Alpha has a lower penetration power so it cannot escape, causing damage to the body.
Never allow skin contact with a source. Aways handle with tongs.
Always store radiation in a lead box as it absorbs all of the radiation.
If someone needs an x-ray, the rest of their body is protected with lead while the part of the body which needs an x-ray is exposed to radiation as it protects the rest of the body.