Broadly speaking, radiation refers to any form of energy that is radiated. This includes stuff like visible light. When we talk about the dangerous stuff that you would associate with nuclear waste or atomic bombs, we refer to a category of radiation called ionizing radiation. This radiation consists of subatomic particles that carry enough energy to knock electrons off of atoms. This is potentially bad for us because it can damage the complex molecules, particularly DNA, that our cells depend on. A large dose of radiation can be outright fatal. At lower doses, the damaged DNA can lead to cancer later in life.
There are a few ways of producing ionizing radiation. One way is through radioactive material. When we say something is radioactive, it means the nuclei of its atoms are unstable. Essentially, the nucleus is in a configuration that has too much energy. It shoots out a high-energy particle, changing into a different atom in the process. Until this happens, it behaves like any other atom.
We are constantly exposed to low doses of ionizing radiation from natural sources, including traces of radioactive material in our bodies. It is only at higher doses that you should be concerned.
This chart here is a helpful guide:
[https://xkcd.com/radiation/](https://xkcd.com/radiation/)
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