Alpha decay was one of the first discoveries of nuclear physics: a heavy
nucleus can decay with the emission of a 
nucleus, or alpha
particle. In fact, decay of heavy nuclei is the source of terrestrial
helium (in particular from oil wells). Uranium, the highest Z
naturally-ocurring element, is widely spread in the environment.
Alpha decay is an important heat source within the earth (and keeps the
core molten). It is an important source of environmental background
radiation (e.g. from the rocks at Clifton, from radon seeping into
enclosed spaces, etc). Alpha emitters have industrial applications (e.g.
smoke detectors).