There are a number of material properties that are commonly derived from a tensile test curve.
The Modulus is a measure of stiffness, so the modulus of a material is very important in applications where the amount of distortion should be small: e.g., for cantilever beams or crankshaft deflection between bearings
This is the most important strength value for design. In most applications it is necessary to stay within the elastic region, so that no permanent deformation due to the load occurs. It is very important for springs and pressure vessels.
This is important for materials in fabrication. High ductility means that they can be shaped easily without breaking in the process. Designers also often want a minimum level of ductility so that if the stress that is applied to the component is too high the material will deform before it breaks.