Alpha radiation is a strong ionizer, but it can only penetrate through few cm of air. How then can alpha particles cause human biological damage?
Alpha particles quickly lose kinetic energy within a short distance of their source. In general, external alpha radiation is not harmful since alpha particles are effectively shielded by a few centimeters of air, a piece of paper, or the thin layer of dead skin cells. Thus external alpha radiation is not harmful per se. But many alpha sources also are accompanied by beta-emitting radio daughters, and alpha emission is also accompanied by gamma photon emission. These are extremely harmful to living cells. If substances emitting alpha particles are ingested, inhaled, injected or introduced through the skin, then it could result in a measurable dose through their ionising effect which eventually changes the polarity of parts of the cells in your body. This then causes your genetic information to become mixed up, causing mutation or death of the cells.