the green trace shows an estimate of current through an inductor as its core becomes saturated.
info here:
http://ludens.cl/Electron/lmeter/lmeter.html
this circuit tries to approximate the effect of saturation in an inductor. once the core is saturated with magnetic flux, the DC current flowing through it cannot magnetise the core any further. the effective inductance of the core reduces significantly! in this example the core begins to saturate at 25mA, and is fully saturated at 80mA.
this means that the amount of current being opposed by the coil drops off, reducing the impedance, and more current flows.
different cores and different materials have different effects. I'm still learning this.
the blue trace shows the idealised inductor in simulation. it does not saturate. but for simulation purposes that's okay as we assume the inductor is suited for the application being simulated.