Why do stars twinkle?

Hint
The atmosphere of the earth acts like a medium that can distort and affect the light coming in from outer space. The refraction of light is a phenomenon where the path of light deviates as it passes through a transparent medium of different refractive index.

Complete step by step answer
Stars are point sources of light which means they are so far away from us that they only appear as points, even when viewed from terrestrial telescopes. The only thing which can be used to determine the identity of a star (In general) is its Intensity.
When stars twinkle, their intensity changes. This is due to the turbulence present in the atmosphere of the earth.
The air molecules follow the Brownian motion, they are always moving in random directions. This means that the density of the atmosphere is not constant throughout. It changes continuously.
The term refractive index ($\eta $) depends on the density and temperature of the material. It can be imagined that the more the number of molecules, the more will be the light deviated from its original path.
So when stars are viewed through the atmosphere, the light waves coming from it are continuously deviated by a small angle. The magnitude and the exact angle depends on the instantaneous density of the atmosphere. And thus the intensity increases and decreases randomly, giving rise to Twinkling.

Note
Unlike stars, planets do not twinkle. This is because planets are not pointing objects, if we see them with a viewing aid, they appear like a disk. So when their light is deviated by a small amount, it reaches another point which also lies on the disk, this happens for all the points present within the disk. And as a result, their Intensity does not change.