When a charged particle moves inside a polarizable medium, it excites some the ellectrons of that medium. As the excited ellectrons return to their ground state, they emits electromagnetic radiation. According to the Huygens principle, the emitted waves move out spherically at the phase velocity of that medium. If the particle moves faster than the speed of light in that medium, the emitted waves add up and at an angle with respect to the particle direction a radiation is emitted which is known as Cherenkov radiation.