Radiation comes from many sources, natural and artificial. There are over 60 naturally occurring radioactive elements. In addition, there are many sources of radiation created by the human race for a variety of purposes.
Unless radiation is very intense, we don't notice it because we have no naturally evolved sense organs to detect alpha, beta and gamma radiation. Exposure is cumulative over time and can have effects that are not noticed until decades after exposure.
There are many sources of gamma rays and highly energetic charged particles in space including our own sun, nova and supernova explosions, and other exotic astronomical phenomena such as pulsars which can direct beams to intense radiation toward the Earth. The Earth's atmosphere filters out a lot of it but some makes it through to the ground. Because the atmosphere is thinner at higher elevations, there is more exposure at high altitudes.
There are radioactive elements all around us. The amount of radioactivity in the soil under our feet varies with the type of soil, the mineral make-up, the density of the soil and the amount of water present. Radon is a colorless and odorless gas which is produced by the decay of natural radioactivity in soil and other materials. It seeps into homes and is the main source of natural radiation exposure. It is the second leading cause of lung cancer.
The radioactivity in the air we breathe can be found in gases and in dust which may come from natural radioactivity in the soil in the form of particle or radon gas, mushroom clouds generated by nuclear explosions and releases of radioactive dust and vapors from nuclear accidents at power plants and waste facilities.
The water we drink contains radioactivity in the form of natural particles from soil through which the water passes and dust washed out of the air by the rain. Radioactive materials are carried by streams and rivers to lakes and the ocean.
Radioactivity finds its way into the plants we eat from the natural radioactivity in the soil and water used to grow them. Radioactivity from the soil and water consumed by animals and from the water, aquatic plants and other aquatic life that fish and crustaceans consume.
Our own bodies take up radioactive materials from the air, the water and the food that we consume. Some of the radioactive materials that we consume are passed out of the body but others accumulate in different tissues.
Nearly half of radiation exposure of the people in the US comes from medical sources such as computer tomography (CT) scans, x-rays and nuclear medicine. Additional exposure can result from improper handling of consumer products that contain radioactive elements such as smoke detectors. Security procedures for transportation have begun to employ devices that produce radiation such as full body scanners at airports.
The radiation produced by nuclear power plants is generally contained except for accidents such as Chernobyl and Fukushima which both released substantial amounts of radioactive materials into the environment that made their way around the world. In addition, the radioactive waste from nuclear power plants and the production of nuclear weapons when improperly handled can make its way into the environment.
So the question is not whether or not we are exposed to radioactivity in the normal course of our daily lives but how much and what type.