Mass-spring system
A simulation model in which an object is a network of point masses joined by springs and dampers.
Divide a sheet of cloth into a grid of point masses and connect neighbours with springs that obey Hooke's law, and you get fabric that stretches, folds and falls. Xavier Provot described the classic arrangement in 1995: structural, shear and bend springs that separately resist stretching, shearing and folding. The same model drives rope, hair and simple soft bodies.
Its weakness is stiff springs. The stiffer the spring, the more easily an explicit integrator blows up, so the system needs small timesteps or implicit integration (Baraff and Witkin, 1998). In games, position-based dynamics has largely taken over for cloth precisely because it stays stable regardless of stiffness — but the mass-spring network is still the model everything else is explained against.