Verlet integration: each particle stores its current and previous position. Velocity is implicit in the difference between the two, giving second-order accuracy without ever computing velocity explicitly. That makes it trivial to satisfy positional constraints after each step, which is exactly what cloth needs.
Constraints enforce fixed distances between neighbors via Gauss-Seidel relaxation. Each pass propagates corrections further across the mesh, so five passes per frame let information travel roughly five links outward. More passes mean stiffer fabric; fewer passes produce stretchy, rubbery behavior.
Tearing works by removing any constraint that stretches past 2.5x its rest length. Once a link breaks it never reforms, so rips propagate naturally along stress lines. The result is realistic failure behavior from a trivially simple rule.
Drag to push particles around. Pull hard and fast to concentrate stress and watch the cloth rip along the path of maximum strain.
Wikipedia