Cherenkov radiation is an effect where charged particles enter a medium faster than the phase velocity of light in that medium. This why is nuclear reactors under water glow blue (not green!). The effect is similar to that of a sonic boom.
As the charged particle enters the medium it has to rapidly slow down to match the speed of light. This causes it to experience photoluminescence where the lost energy from the charged particle is emitted as light emission.
These light emissions propogate as a spherical wave front. When the velocity of the particle is less than the speed of light in that medium (ie. %% \nu_p < \frac{c}{n} %%) these wavefront do not cross and so there are no interference effects.
However, when %% \nu_p > \frac{c}{n} %% these wavefront do overlap and so there is constructive interference which leads to a cone-like light signal.
This is a great analogy to sound wave where at the point of a sonic-boom one can observe a cone of a sound wave away from the plane. Using some basic trigonometry we can define the speed of the particle using the angle the cone creates also known as the Cherenkov emission angle.
In other words by measuring the angle the cone creates we can find out the speed the particle is travelling at. This principle forms the foundation of many different experiments. For example at the Large Hadron Collider at CERN there is an experiment called ALICE (A Large Ion Collider Experiment). This detector directs the particles from a high speed collision into a medium with a known refractive index and by measuring the angle of the Cherenkov emission angle the speed of the particle can be determined. This enables us to make some determinations as to the nature of this particle.