Short answers, pulled from the story.
Élie Cartan introduced the torsion tensor in 1923 as a vector-valued 2-form derived from an affine connection. This mathematical object measures how a tangent space displaces when rolled along an infinitesimal parallelogram with sides X and Y.
The torsion tensor quantifies slipping or twisting during the rolling process of a tangent space along an infinitesimal loop. It represents the failure of a parallelogram to close in the tangent space, resulting in a displacement vector T(X,Y) that shifts the final point away from the start.
Einstein-Cartan theory implements non-zero torsion within gravitational physics to unify gravity with quantum spin while standard general relativity assumes zero torsion via the Levi-Civita connection. Spin density acts as a source for torsion much like mass-energy sources curvature in Einstein's original formulation.
Energy-minimizing states cause pairs of elastic filaments twisted around one another to adopt helical shapes while length-maximizing configurations stretch them straight. Torsion reflects differences between these competing geometric preferences during biological development and material deformation processes.