Stars appear to pulsate and twinkle in the night sky due to the refraction of light through the Earth's atmosphere. When the light from a star enters the atmosphere, air molecules bounce and deflect the light rays, slightly altering the apparent position and intensity of the star.
The reason stars twinkle and planets don't is because of their relative size in the sky. Stars are so distant that the human eye resolves them as single points of light, and the refraction effect causes each point of light to appear to move. Planets, on the other hand, appear considerably larger, allowing the eye to smooth out refractive differences and perceive the incoming light as a solid disc.