Kerr microscopy is based on the magneto-optical Kerr effect, which causes a rotation of linearly polarized light on reflection from a magnetic material
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If the linearly polarized light enters the surface of non-magnetic material, it causes the oscillation of elections in the incident plane. They re-emit light in direction of reflection with the same orientation of polarization plane.
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In magnetic material the oscillating electrons experience Lorentz force, that induces additional oscillation of electrons in transverse direction. This additional oscillations are seen as Kerr amplitude transverse to initial one, which together with normal E-vector results in rotation of polarization plane CW or CCE depending on the orientation of the magnetization within the surface plane.
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Blocking the light from one domain phase using an analyzer creates domain contrast in an optical polarization microscope. Light from the domain with one particular magnetization, rotated counterclockwise, is completely blocked, while the light from the domain with the opposite orientation of magnetization, rotated clockwise partially passes through the analyzer.