Quantum or Particle Theory:

You know that as per to the quantum theory of radiation, an electromagnetic radiation is considered to be consisting of a stream of particles known as photons. Photons constituting a radiation of frequency ν would have energy equivalent to hν although h is the Planck's constant. The interaction of the radiation along with the interacting species could be visualised in terms of collisions among them and the photons. If the collisions are elastic (That is they do not included any exchange of energy) the photons would be scattered (deflected) with their incident frequency remaining unchanged. This explains the observance of Rayleigh line in the spectrum. Since most of the collisions are elastic in nature, most of the scattered photons will have similar frequency as the incident frequency. Thus the Rayleigh line is observed to be quite intense.

A little fraction of the collisions among the photons and particles of matter are found to be inelastic in nature that is these includes exchange of energy. While the photons constituting the radiation undergo inelastic collisions along with the absorbing species, they either gain or lose energy. Those energy exchanges bring about transitions within the quantised energy stages of the molecules. In like an event of inelastic collisions, the molecules are either vibrationally (and/or rotationally) excited or they might undergo vibrational (and/or rotational) relaxation. Within both the cases the photons get scattered along with a frequency variant from their initial frequency. In former case i.e., while the molecules undergo excitation, they are of lower frequency. In the last case, whereas the molecules undergo relaxation, scattered photons are of a higher frequency. These scattered photons provide rise, respectively to the Stokes and anti-Stokes Raman lines within the spectrum.