Torsion is a fundamental concept in mathematics and physics, particularly within the realms of geometry and mechanics. In its simplest form, torsion refers to the twisting or rotation that occurs along a curve or surface. This property is critical in understanding the behavior of materials under stress, as well as in the study of complex geometrical structures.

In differential geometry, torsion describes how a curve deviates from being planar. It quantifies the rate at which the curve's tangent vector rotates around the curve’s principal normal vector. This measurement is essential for defining the curvature and overall shape of a space, contributing significantly to fields like general relativity and continuum mechanics.

Moreover, torsion plays a crucial role in the theory of elasticity, where it helps engineers predict how materials will deform under twisting forces. For instance, in designing components such as shafts or beams, understanding torsion allows for the creation of more efficient and resilient structures.

Overall, the concept of torsion bridges pure mathematical theory with practical applications, making it an indispensable tool across multiple disciplines.