What is a radiation dose?
The concept of a dose may often bring to mind a medical administration of a chemical to treat or mitigate some medical condition or symptoms. When most medical doses are prescribed, they are in many cases scaled to the weight of the person receiving the medication. If you think of the medicine as having a given chemical potential energy, then the prescribed dose would be in the form of energy per mass. Based on this concept, there are known safe limits for the doses proscribed to patients so that the normalized dose gives the same effect to different people.
Hearing protection also follows a similar form of dose. The energy in sound waves has prescribed limits for the dose to the ear drum. Rather than call out the exposure time to various decibel values of sound intensity, decibel levels are generally compared to more familiar sounds such as talking, a vacuum cleaner or even a jet engine. Radiation dose is similar in that rather than listing off levels of rem or millirem (where 1000 millirem = 1 rem) for various exposures to a person, the values are typically compared to more familiar exposure events such as breathing fresh mountain air (with all the radon the lungs take in) to a much smaller exposure such as walking past an airport luggage scanning system.
When it comes to radiation dose, the units are in terms of the energy imparted per mass of tissue exposed. When the units are in rem, millirem or even Seiverts (Sv), milliSeiverts (mSv) and so on, this means that the type of radiation is normalized to an equivalent biological effect. Alpha particles (helium nuclei) and neutrons typically have a much higher biological effect than to beta particles (electrons) and gamma rays (photons). Why this is significant is that when dose is expressed in these units of rem or Sv, the biological effect is now on equal footing from equal doses. In other words, the same dose from eating potassium (which is naturally radioactive) in healthy foods would be equal to a scaled ingestion of radioactive cesium.
As an example, being up in the Rocky Mountains, the granite from which the name derives has a relatively high concentration of Uranium and Radium so that the radon in the air would give a resident more than a few hundred millirem every year. Radon and all of its decay products normally in air are heavy metals which emit highly energetic alpha and beta particles along with high energy gamma rays. The dose from plutonium particles, americium particles and radon decay particles are all on identical footing in terms of risk when expressed in units of dose equivalent such as rem.
One could get a higher dose from radon if exposed to higher levels of radon just as one could get a lower dose from plutonium particles if exposed to lower levels of the same. Dose is important in that it already incorporates all the risk factors in terms of either cancer or acute radiation syndrome. Noting here that individual cancer risk does not even make sense due to the nature of the effect unless a radiation dose is already around 10 rem (or equivalently 10,000 millirem). Similarly, acute radiation syndrome does not start to be a concern until a dose of around 100 rem has been received.
It is because of this that typical reports of radiation exposure are not given in units of millirem as people are not familiar with that term but rather in things like the equivalent of a dental x-ray or the equivalent of a jet airplane flight as each of these will only give a few millirem.
Just because radiation can be dangerous does not mean that any radiation is dangerous. It really does depend on the dose, whether the dose is natural in origin (such as internal potassium which is radioactive giving off high energy beta and gamma radiation) or manmade in origin (such as medical or industrial sources), the value of the dose is what determines the relative risk from any exposure to radiation (or pretty much anything else for that matter).
The biological effect in terms of energy imparted per unit mass of tissue is in truth the scientific definition of dose yet it is not necessarily something many people can interpret. Being able to say the radon decay products you breath in fresh mountain air gives almost a millirem per day from breathing is simply a more familiar scale as are dental and medical x-ray exposures. When public officials describe radiological effect in terms of dose and compare these to more familiar sources of radiation, it is strictly an attempt to communicate risk in a nontechnical way while still being accurate.
The technical terms would be to say effective or equivalent dose are expressed in units of rem and millirem give the same exact risk whether the source is natural, industrial or medical, by definition (hence the reason radiation scientists, physicians and health physicists all use it).