Internally, ferromagnetic materials have a structure that is divided into domains, each of which is a region of uniform magnetization.  When a magnetic field is applied, the boundaries between the domains shift and the domains rotate; both of these effects cause a change in the materials dimensions.  The reason that a change in the magnetic domains of a material results in a change in the materials dimensions is a consequence of magnetocrystalline anisotropy; it takes more energy to magnetize a crystalline material in one direction than in another.  If a magnetic field is applied to the material at an angle to an easy axis of magnetization, the material will tend to rearrange its structure so that an easy axis is aligned with the field to minimize the free energy of the system.  Since different crystal directions are associated with different lengths, this effect induces a strain in the material.
The reciprocal effect, the change of the magnetic susceptibility (response to an applied field) of a material when subjected to a mechanical stress, is called the Villari effect. Two other effects are related to magnetostriction: the Matteucci effect is the creation of a helical anisotropy of the susceptibility of a magnetostrictive material when subjected to a torque and the Wiedemann effect is the twisting of these materials when a helical magnetic field is applied to them.
The Villari reversal is the change in sign of the magnetostriction of iron from positive to negative when exposed to magnetic fields of approximately 40 kA/m.
On magnetization, a magnetic material undergoes changes in volume which are small: of the order 10.