What is rotational transform?
Rotational transform is the motion of the magnetic field lines the short way around the torus while they are also wrapping the long way around the torus. That is in the above 2 figures, the magnetic field lines do not in general simply come back to the same point and close on themselves, but they are displaced by some amount so that over many times around the torus they will completely cover it. This must be qualified by the fact that there are always some “rational surfaces” where the field lines do eventually (after multiple circuits around the torus) close on themselves.