magnetization
Ordinary matter is riddled with microscopic current loops — electrons orbiting and spinning — each a tiny magnetic dipole. Usually they point every which way and cancel, but a field, or spontaneous order in a ferromagnet, can line them up. Magnetization is the net magnetic dipole moment per unit volume that results.
The magnetization M is defined as the magnetic dipole moment per unit volume of the material. Its effect on the large-scale field is captured by bound currents: a magnetization gives a bound volume current density J_b = curl M and a bound surface current K_b = M x n. These are perfectly real currents — they produce genuine magnetic fields — but they arise from the aligned microscopic loops rather than from charge flowing through a wire. M enters the auxiliary field H through H = B/mu_0 - M, equivalently B = mu_0 (H + M).
Magnetization is the magnetic counterpart of the electric polarization P, and the parallel is close but not perfect. In a linear magnetic material M = chi_m H, with chi_m the magnetic susceptibility: positive and tiny for paramagnets, small and negative for diamagnets (which oppose the field). Ferromagnets break the linear rule entirely — they retain magnetization after the field is removed (hysteresis), which is what makes permanent magnets and magnetic memory possible.
A uniformly magnetized bar magnet has M constant inside, so its bound volume current J_b = curl M vanishes there, and all the current sits on the surface as K_b = M x n. That surface current is a solenoid-like sheet wrapping the magnet — which is exactly why a bar magnet's external field looks like a solenoid's.
M is dipole moment per volume; it acts through bound currents J_b = curl M and enters H = B/mu_0 - M.
Bound currents from magnetization are as real as free currents — they make genuine magnetic fields — they simply are not free to be driven by an external circuit. In a ferromagnet M is not proportional to H and depends on history (hysteresis), so the linear relation M = chi_m H fails.