The principle describes the relationship between the force required to extend or compress an elastic object, such as a spring, and the resulting distance of that deformation. It establishes that the magnitude of the force is directly proportional to the distance the object is stretched or compressed, provided the material remains within its elastic limit. Mathematically, this relationship is represented by a linear equation where the constant of proportionality, known as the spring constant, is characteristic of the material and its geometry. This concept is fundamental in materials science and physics for analyzing the behavior of springs and other elastic media under stress.