Exposure to ionizing radiation is considered to be dangerous for humans. The rays or particles can do damage to human tissue to an extent that is dose dependent: the more radiation, the more damage. One theory on the relationship between absorbed radiation dose and the probability of health effects is that it is linear without threshold, which would mean that there is a possible risk of health effects with any dose, however small.
While there may indeed be no absolutely safe dose, but there are dosages that are considered acceptable for practical purposes and unlikely to produce health effects. The risk of exposure is also dependent to a certain degree on the length of time over which the exposure occurred. The body can tolerate small doses that add up over time better than the same exposure all at once.
All humans are exposed to some radiation simply by living on earth. This naturally occurring or "background" radiation comes from the radioactive decay of naturally occurring radioactive elements in the earth's crust.
In addition to this, other sources of radiation are part of the course of everyday life: dental or medical X rays, microwave radiation, luminous watch dials, color televisions, cosmic radiation, smoke alarms, exit signs; a variety of sources of exposure to extremely small doses which add up slowly over time since dosage of radiation is cumulative over a lifetime.
When an exposure occurs over an extended period of time, it is referred to as "Chronic Exposure". All of us are chronically exposed to radiation naturally and in the course of daily life.
Persons working in the nuclear industry or utilizing a radiation source in the course of their work receive additional exposure. Standards have been set to protect such workers from dangerous dosages of radiation. However, these standards tend to change (lower) as more is learned about the effects of radiation on the human body.