Hi,
The tanh() function models the BH curve, with H as the x axis and B as the y axis.
Since H is proportional to the current I, x would be the current through the inductor or at least proportional to current.
If you do a 2d plot of tanh(x) from say -5 to +5 you can see an entire anisotropic BH curve.
This kind of BH curve is called an "anisotropic" BH curve. Unlike a pure inductance that has a perfectly linear curve (straight line) it models saturation, but it does not model hysteresis. It does allow for faster calculations though.