Radiation is a process in which energetic particles or energetic waves travel through a medium or space. Radiation is not some mysterious, arcane force. It is a known quantity, found everywhere: on Earth, in space and on Mars.
Radiation on Earth
On Earth, you are constantly exposed to radiation. This radiation comes from sources inside your body, the buildings you live and work in, from the air, from the Earth itself, and from cosmic rays.
Radiation in Space
Astronauts who are in space are exposed to more radiation than people on Earth. Earth's magnetic field and atmosphere significantly reduce the amount of radiation that makes it through to the surface of the planet. En route to Mars, however, our astronauts won't have this protection.
For this reason, we need to provide protection to the astronauts, by shielding them. They will receive general protection from the structure of the Mars Transit Habitat during space flight. The Transit Habitat will also contain a dedicated radiation shelter, which will protect the astronauts with much more shielding than the habitat. The astronauts can also sleep in the radiation shelter.
A major source of radiation exposure en route to Mars is caused by Solar Particle Events (SPEs). During a SPE, the sun ejects very large quantities of energetic particles which, in the absence of proper shielding, can lead to acute radiation poisoning. The astronauts should expect, on average, one SPE every two months [US dept. of commerce reference], meaning an expected total of three or four during their 7 month trip. Not all SPE's are large enough to be dangerous. Large Events generally occur only once or twice every solar cycle, which has a period of about 11 years [NASA JSC reference].
To minimize exposure, the crew would be restricted to a radiation shelter during the most intense phase of an SPE. However, these highly intense phases usually only last for a few hours, meaning that comfort in the shelter is not a huge priority, and relatively low-volume radiation shelters are feasible [NASA JSC reference].
Considering the largest event measured to date, in August 1972, at least 20 g/cm2 of shielding would be required to remain below the 30-day limit, [ESA reference (PDF)] [NASA JSC reference]. The Mars One Transit Habitat radiation shelter will have at least 20 g/cm2 of shielding.
Radiation on Mars
On Mars, the thin atmosphere and absence of a protective magnetic field results in higher radiation on the surface compared to that of the Earth. For this reason, the habitat will be covered by several meters of soil, increasing the shielding dramatically. Just five meters of soil provides the same protection as the Earth's atmosphere (1,000 g/cm2).
When the astronauts go outside, they will wear a Mars suit, which will also give them some protection against radiation. During SPEs, the astronauts will return to the habitat for protection.
How bad is radiation?
All humans are exposed to radiation, even from sources inside their bodies. What are the health risks that the astronauts take?
Radiation is obviously a concern during spaceflight. However, many advances were made for the Mir and ISS stations, where astronauts have lived for many months. For example, Valeri Polyakov stayed on Mir for 438 days on one occasion, and for 241 days on another; Sergei Avdeyev stayed on Mir for 380 days; Michael Lopez-Algeria and Mikhail Tyurin stayed on the ISS for 215 days; Gennady Padalka stayed on both Mir and the ISS for 199 days each. These and other astronauts have proven that long-duration space flight is possible without human sacrifice.
As described in an FAA and university study from 2005, a journey to Mars and back (in the case of the study, totalling 536 days in space) would mean the chance of contracting cancer for 25-34 year-olds is around 10% for men, and 17% for women.
But let's compare it to people who do not go to Mars. In their lifetimes, men have a 12% chance of contracting prostate cancer, and women have 12.5% chance of developing breast cancer (UK study 2008).
Or let's compare it to people who smoke: Smoking more than 5 cigarettes a day leads to a 24.6% chance of developing lung cancer for men in their lifetimes, and 18.5% for women (European study 2006).
Finally, our astronauts will spend only 210-220 days in space, compared to the 536 days in the study mentioned above. Staying on Mars will result in much lower doses, even if the astronauts stay for a long time.
Most of the radiation risk is expected during the spaceflight portion of a Mars mission. There is a risk of increased exposure to radiation during Mars missions, but the risk can be severely mitigated by adequate shielding. ESA and NASA studies confirm that the radiation risk is very manageable.