Faraday effect states that magnetic field can affect the polarization of a linearly-polarized light.
Consider a linearly-polarized (LP) light passing through a pair of Helmholtz coils (along the direction of the magnetic field). Let’s decompose the LP light into its components: Left- and right-handed circular beams (LHC and RHC).
The electric field of each component exert a force on electrons which leads to their circular motion (how?). This motion creates a magnetic field in or against the direction of the applied magnetic field. This means different interaction of LHC and RHC beams with the applied magnetic field which results in a different refraction index and consequently a different propagation speed for LHC and RHC beams.
Combining back the two components (LHC and RHC) of the beam after the coils, produces a linearly-polarized light with a polarization angle different from the beam entered the magnetic field. This change in polarization angle is called “Faraday rotation”.