There have been no reports of short-term effects or symptoms caused by radon exposure. The only reported long-term effect is lung cancer. If you inhale a radon atom, the atom can disintegrate while it is in your lungs. When it disintegrates, it becomes polonium-218, which is a metal. This metal atom can settle in your lungs, and over the next hour or so it will emit a number of alpha particles, beta particles and gamma rays. It eventually turns into lead-210 with a half-life of 22 years, which is fairly stable in this context. But now you have an atom of lead in your system, which causes its own problems. It is the quick, hourlong sequence of alpha, beta and gamma emissions that can lead to the mutations in the lung tissue, which can cause cancer. Smoking enormously increases the risk of lung cancer from radon exposure.
So you can see that a high concentration of radon gas, despite the fact that it is completely natural, is not something you want in your home.