Also called the Magneto-Optic Effect, it was first described in 1845 by Michael Faraday and occurs in most optically transparent dielectric materials (including liquids) when they are subject to strong magnetic fields. The effect is able to rotate the plane of polarization of an input beam which propagates parallel to the direction of the magnetic field in the material. The angle of rotation is given by:
Where B is the magnetic field in tesla, V is the verdet constant for the material, and d is the effective length of material contained within the magnetic field (although due to the nature of most practical magnetic fields, this can sometimes be difficult to ascertain with any certainty). Unlike the electro-optic effect, the magneto-optic effect causes a true rotation of the plane of polarization for any input polarization angle.
The Faraday effect is a result of ferromagnetic resonance when the permeability is represented by a tensor. The mathmatical details are beyond the scope of this site, however, Amnon Yariv's "Quantum Electonics" is a good starting place for how it all works.
The Faraday Effect is used to build Faraday rotators which, in turn, are the most importantc omponent of Faraday Isolators.