The linear relation

$$B=\mu H$$

is only an approximation for ferromagnetic materials. As the magnetizing field increases, the material eventually reaches a region where further increases in $H$ produce much smaller increases in $B$. This is magnetic saturation.

The magnetization curve

At low and moderate field levels, domain alignment can make the effective permeability large. As more domains become aligned, fewer remain available to respond, so the $B$-$H$ curve bends and its slope decreases.

Effect on magnetic circuits

In the unsaturated region, reluctance can often be treated as approximately constant. Near saturation, permeability is no longer constant, so

$$\Phi=\frac{NI}{\mathcal R}$$

is no longer a simple linear relationship between current and flux.

A large increase in current may then produce only a modest increase in flux.

Why saturation matters

Transformer and machine cores are designed to operate below excessive saturation under normal conditions. Saturation can increase magnetizing current, distort waveforms, change inductance and produce additional losses and heating.

Saturation is therefore not merely a material detail; it changes the electrical behavior of devices that rely on magnetic cores.