The permittivity of a given media depends on the electric susceptibility of the media, which can be considered a measure of how easily the media is polarised by the application of an external electric field. Now in general, when an electric field is applied to dielectric media, the media will not polarise instantaneously. In other words, polarisation occurs some time after the electric field was initially applied, this results in a so-called 'phase difference' between the frequency of the applied electric field and the polarisation of the dielectric media.
The refractive index is defined as the ratio of the speed of light in vacuum to the phase velocity of light in the dielectric media. The phase velocity of light is a function of the permittivity and permeability of the media.
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