Why is radiation dangerous? From Wikipedia:

Exposure to radiation causes damage to living tissue; high doses result in Acute radiation syndrome (ARS), with skin burns, hair loss, internal organ failure and death, while any dose may result in an increased chance of cancer and genetic damage

Why exactly is radiation dangerous for people and animals? I see a lot of mentions regarding danger of radiation on the Internet but I couldn't find any detailed info on how exactly does it affect cells of an animal in a way that exposes them to a cancer or other health issues.
Are different radiation sources (i.e. cosmic radiation or radiation emitted from a nuclear reactor) affect health in different ways? Are some animals more resistant than others and if so, which attributes are responsible for that?
 A: The fundamental physical reason is that ionizing radiation damages and destroys molecules, and the chief way it does this is by blowing apart the bonds that hold them together. The reason it can do this is that the individual particles of such radiation - e.g. photons (gamma), or electrons (beta) - have enough energy to burst at least one such bond, and almost always many, many bonds. The fact that it is the individual particles which have this energy is crucial: the light from a light bulb hitting your skin has a total energy that is strong enough to in theory be useful to destroy many, many, many bonds, but it doesn't, because molecules absorb energy on a per-particle basis and the individual particles are low-energy enough as to not do so.
The fundamental biological reason is that biology depends on the tightly-synchronized, ordered operation of numerous molecular processes occurring all throughout the entire organism. If you damage or destroy a molecule, that does all of rendering it incapable of participating in the usual processes it otherwise would, disrupts those processes, and perhaps the molecular fragments cause new, unwanted processes to occur.
Now, biological systems are resilient and even anti-fragile in the sense that if these processes are disturbed by some amount - if they were not, they could not persist at all - that is, they can restore themselves to a healthy condition (resilience), and moreover, even adapt to weather a future insult better (anti-fragility) if given the chance, however there is only a limited amount of such survival capacity: push things far enough and hard enough, and they, like everything else, break. If you damage too many molecules too fast for these reparative processes to work, you both disrupt enough vital processes and introduce enough new, unwanted ones that the whole house of cards starts falling apart and the reactions begin to march inexorably from organized choreography toward entropic, stewing uselessness: i.e. death.
For example, if we consider only electromagnetic radiation, i.e. photons, we can use that that the typical energy of a chemical bond is around 5 eV or 0.75 aJ, and
$$E_\mathrm{photon} := hf$$
Thus we get a frequency $f$ of $f = \frac{E_\mathrm{photon}}{h} = \frac{0.75\ \mathrm{aJ}}{0.626\ \mathrm{aJ/(PHz)}} \approx 1.2\ \mathrm{PHz}$, which is roughly that of the beginning of UV-C rays, or "germicidal light", and hence the name. This is also, not coincidental. All of X-rays and gamma radiation emissions from radioactive materials are far in excess of this, on the order of $10^6\ \mathrm{aJ}$ per particle or beyond, and thus are capable of potentially breaking thousands to millions of chemical bonds each, and/or exploding entire complex molecules with a single impact in a hail of reactive debris - and hence their notorious reputations for deadliness.
A: @David White is correct. This is a very broad question.
Radiation, or more specifically, electromagnetic radiation, covers a broad range from very low frequency long wavelength radio waves that pass right through you with no interaction to very high frequency short wavelength radiation that can cause severe biological damage, and everything else in between.
In addition to David Whites link, I suggest you Google "interaction of electromagnetic radiation with matter" and check out the Hyperphysics website on the subject. It provides a very good overview how radiation interacts with matter from a physics standpoint more that a biological standpoint. It covers the interaction of low frequency radio waves, microwaves, infra red, ultraviolet, etc. with matter. The combination of this link and the radiobiology link should give you a good perspective.
Hope this helps.
