Why does a magnetic core saturate? What is its actual mechanism?
Ferromagnetic materials like iron that show saturation are composed of microscopic regions called magnetic domains that act like tiny permanent magnets. Before an external magnetic field is applied to the material, the domains are oriented in random directions. Their tiny magnetic fields point in random directions and cancel each other out, so the material has no overall net magnetic field. When an external magnetizing field H is applied to the material, it penetrates the material and aligns the domains, causing their tiny magnetic fields to turn and align parallel to the external field, adding together to create a large magnetic field which extends out from the material. This is called magnetization. The stronger the external magnetic field, the more the domains align. Saturation occurs when practically all the domains are lined up, so further increases in applied field can't cause further alignment of the domains. This is a simplified account; a more complete explanation can be found in Ferromagnetism.