Young's modulus is a measure of a material's stiffness, defined as the ratio of tensile stress to strain during elastic deformation. It indicates how much a material will stretch under a given load, with the elastic range extending from no load to the yield stress. Ductility refers to a material's ability to stretch without breaking, while malleability describes its capacity to deform under compression. The discussion highlights confusion surrounding Searle's apparatus and the lack of depth in educational resources on these topics. Understanding these properties is essential for A-level physics students.