This point can be seen in figure 1 below where the line changes from linear to curved behavior. The linear behavior is characterized by Young's modulus. In this region strain is directly proportional to stress. In plastic deformation strain relates to stress in a power law form. This power law form is due to work or strain hardening.
Work hardening is a process by which the material grows stronger as it is deformed.
This phenomena happens because microscopic defects in the material interact to make the strain of the material harder to achieve. At the maximum in figure 1 the amount of stress needed for further strain decreases. Necking is a decrease in the local area of sample due to a localization in stress. When a material is plastically deformed too much the material pulls apart through a ductile fracture process. In this process voids start to form which further weaken the material and increase the local stress which eventually tears the material apart.