The American Cancer Society has a very clear and informative discussion of radon and the hazards associated with it.  I've reproduced a portion of their article below.  You can read the entire article here.

What is radon?

Radon is a colorless, odorless, radioactive gas. It forms naturally from the decay of radioactive elements, such as uranium, which are found at different levels in soil and rock throughout the world. Radon gas in the soil and rock can move into the air and into ground water and surface water.

Radon is present outdoors and indoors. It is normally found at very low levels in outdoor air and in drinking water from rivers and lakes. It can be found at higher levels in the air in houses and other buildings, as well as in water from underground sources, such as well water.

Radon breaks down (decays) into solid radioactive elements called radon progeny (such as polonium-218, polonium-214, and lead-214). Radon progeny can attach to dust and other particles and can be breathed into the lungs. As radon and radon progeny in the air break down, they give off alpha particles, a form of high-energy radiation that can damage the DNA inside the body's cells.

How are people exposed to radon?

At home and in other buildings

For both adults and children, most exposure to radon comes from being indoors in homes, commercial buildings, schools, and other places. The levels of radon in homes and other buildings depend on the characteristics of the rock and soil in the area. As a result, radon levels vary greatly in different parts of the United States, even within neighborhoods. Elevated radon levels have been found in every state.

The radon gas given off by soil or rock can enter buildings through cracks in floors or walls; construction joints; or gaps in foundations around pipes, wires, or pumps. Radon levels are usually highest in the basement or crawl space. This level is closest to the soil or rock that is the source of the radon. Therefore, people who spend much of their time in basement rooms at home or at work have a greater risk for being exposed.

Small amounts of radon can also be released from the water supply into the air, especially if the water source is underground. As the radon moves from the water to air, it can be inhaled. Water that comes from deep, underground wells in rock may have higher levels of radon, whereas surface water (drawn from lakes or rivers) usually has very low radon levels. For the most part, water does not contribute much to overall exposure to radon.

Radon exposure can also occur from some building materials if they are made from radon-containing substances. Almost any building material made from natural substances, including concrete and wallboard, may give off some level of radon. In most cases these levels are very low, but in a few instances these materials may contribute significantly to radon exposure.

Some granite countertops may expose people to different levels of radon. Most health and radiation experts agree that while a small portion of granite countertops may give off increased levels of radon, most countertops give off extremely low levels. People concerned about radon from countertops and from other household sources can test these levels using home detection kits or by hiring a professional to do the testing (see the section, "How can I avoid exposure to radon?" below).

Radon levels in the air are measured by units of radioactivity per volume of air. The most common measure used is picocuries per liter (pCi/L). According to the US Environmental Protection Agency (EPA), the average indoor radon level is about 1.3 pCi/L. People should take action to lower radon levels in the home if the level is 4.0 pCi/L or higher. The EPA estimates that nearly 1 out of every 15 homes in the United States may have elevated radon levels.

Outdoors, radon generally disperses and does not reach high levels. Average levels of radon outdoors, according to the EPA, are about 0.4 pCi/L.

At certain jobs

In the workplace, people working underground, such as some types of miners, are among the most likely to be exposed to high levels of radon. High death rates from lung problems among miners in some parts of the world were first noted hundreds of years ago, long before people knew what radon was. Studies of radon-exposed miners during the 1950s and 1960s confirmed the link between radon exposure and lung cancer.

Higher levels of radon exposure are also more likely for people who work in uranium processing factories or who come in contact with phosphate fertilizers, which may have high levels of radium (an element that can break down into radon).

Does radon cause cancer?

Long-term exposure to radon can lead to lung cancer. Radon in the air breaks down quickly, giving off tiny radioactive particles (radon progeny). When inhaled, these particles can lodge in the lining of the lungs, where they can damage the cells there. This may eventually lead to lung cancer.

Cigarette smoking is by far the most common cause of lung cancer in the United States, but radon is the second leading cause. Scientists estimate that about 20,000 lung cancer deaths per year are related to radon.

Exposure to the combination of radon gas and cigarette smoke creates a greater risk for lung cancer than either factor alone. Most radon-related lung cancers occur among smokers. However, radon is also thought to cause a significant number of lung cancer deaths among non-smokers in the United States each year.

Some studies have suggested that radon exposure may be linked to other types of cancer as well. But the evidence for such links has been inconsistent and not nearly as strong as it is for lung cancer. Because radon and its progeny are absorbed mainly by inhaling, and because the alpha particles they give off travel only a short distance, it is unlikely they would affect other tissues in the body.

The evidence that radon causes lung cancer comes from studies in people and studies done in the lab.

Studies in people

Several types of studies in people have found that exposure to radon increases lung cancer risk:

These studies have also been used to estimate the amount of risk from different radon exposure levels.

Studies done in the lab

Studies in lab animals have also shown a risk of lung cancer with exposure to radon. These studies revealed that breathing in radon and its progeny significantly increase the risk of lung tumors. In lab studies using human cells, radon and its progeny have also been shown to cause damage to chromosomes (packets of DNA) and other types cellular damage. These types of changes are often seen in cancer cells.

What expert agencies say

Several agencies (national and international) study different substances in the environment to determine if they can cause cancer. (A substance that causes cancer or helps cancer grow is called a carcinogen.) The American Cancer Society looks to these organizations to evaluate the risks based on evidence from laboratory, animal, and human research studies.

Based on animal and human evidence, several expert agencies have evaluated the cancer-causing potential of radon.

The International Agency for Research on Cancer (IARC) is part of the World Health Organization (WHO). Its major goal is to identify causes of cancer. Based on the data available, IARC classifies radon and its progeny as "carcinogenic to humans".

The National Toxicology Program (NTP) is formed from parts of several different US government agencies, including the National Institutes of Health (NIH), the Centers for Disease Control and Prevention (CDC), and the Food and Drug Administration (FDA). The NTP has classified radon as "known to be a human carcinogen".

The US Environmental Protection Agency (EPA) monitors the human health effects from exposure to various substances in the environment. The EPA lists radon as the number one cause of lung cancer among non-smokers, estimating it is responsible for about 20,000 lung cancer deaths every year.

(For more information on the classification systems used by these agencies, see our document, Known and Probable Human Carcinogens.)

Does radon cause any other health problems?

Some studies of miners have suggested a link between radon exposure and some non-cancerous respiratory diseases, especially pulmonary fibrosis (scar tissue forming in the lungs that leads to shortness of breath). These effects appear mainly in miners with high levels of exposure. It's not clear that the lower levels commonly seen in homes can cause the same types of problems.

Can I avoid exposure to radon?

Radon is in the air we breathe, both indoors and out, so it is not possible to avoid it completely. But there may be things you can do to lower your exposure.

For most people, the largest potential source of radon exposure is in the home. You can check radon levels in your home to determine if you need to take steps to lower them. Do-it-yourself radon detection kits can be ordered through the mail or bought in hardware or home supply stores. The kits are placed in the home for a period of time and then mailed to a lab for analysis. Short-term kits are usually left in place for several days before being mailed. Long-term kits, which may give a more accurate assessment of average radon levels over the course of a year, are usually left in place for at least 3 months.

Another way to test radon levels in your home is to hire a professional. Qualified contractors can be found through state radon offices, which are listed on the EPA web site at www.epa.gov/radon/whereyoulive.html.

The EPA recommends taking steps to lower radon levels if test results show levels of 4.0 pCi/L or higher. This value refers to the annual average. If you are using a do-it-yourself test, the EPA recommends using a short-term kit first. If the test result is 4.0 pCi/L or higher, do a follow-up test with either a long-term or short-term kit to be sure. If the result is still high, you should take steps to fix the problem.

A variety of methods can be used to reduce radon levels in your home, such as sealing cracks in floors and walls or increasing ventilation through "sub-slab depressurization" using pipes and fans. The EPA recommends that you have a qualified contractor fix your home because lowering high radon levels requires specific technical knowledge and special skills. Without the proper equipment or technical knowledge, you could actually increase your radon level or create other potential hazards and additional costs. Qualified contractors can be located through state radon offices, which are listed on the EPA web site at www.epa.gov/radon/whereyoulive.html. If you decide to do the work yourself, be sure you have the proper training and equipment.

Certain building materials may be more "radon tight" and may help reduce exposure in areas where radon levels are high. You can get more information from state radon offices or from qualified contractors.