When a material deforms, it does so in several stages. The first stage, called the elastic region of deformation, is linear in nature and not permanent. A stress can be applied, and once it's removed, the material will regain all of the deformation. The second stage, plastic deformation, is permanent. A material that has been stressed into the plastic region will regain the elastic deformation, but will permanently maintain the plastic.
The proportional strength is the point at which plastic deformation begins.