Principal stresses are the maximum and minimum normal stresses experienced at a point in a material. They occur when external forces are applied, causing the material to deform. Understanding principal stresses is crucial in engineering and materials science, as it helps predict failure points and ensures structural integrity. To determine principal stresses, engineers use mathematical methods, such as Mohr's Circle, which graphically represents stress states. By identifying these stresses, engineers can design safer structures and components, ensuring they can withstand applied loads without failing.