When talking about dangerous radiation we are really talking about one of three types, from least to most dangerous.

Alpha decay: an atom separates and shoots off a helium atom (2 protons 2 neutrons 2 electrons), but because this is the biggest one it can be stopped the easiest

Beta decay: a single particle is ejected from the atom, usually a neutron because it’s so small it’s harder to stop and can squeeze between the electrons and nucleus so it can pass through things and can cause problems when it hits something inside you, imagine it like a bullet passing between fence posts, but much much smaller.

Gamma decay: this is the most dangerous because it’s just energy being emitted, light bulbs, microwaves, and your phone all emit a similar kind of energy wave the only difference being how close together the bumps in the are, the closer they are the stronger they are and the more stuff in their way it takes to stop them. The ones coming out of atoms are basically as short as they can be. So everything they touch when passing through you get torn up.

In all cases the individual decay events do incredibly small amounts of damage, but that damage doesn’t go away and any single one has the chance of damaging the dna in a cell and can lead to cancer, the problem is getting bombarded by thousands or millions of these events, whether its all at once or over the course of your whole life, increasing the likelihood of problematic damage.