(a) The refraction of light caused by the earth's atmosphere is called atmospheric refraction. Atmospheric refraction is caused by the bending of light rays when they pass through the layers of the earth's atmosphere, which are of different optical densities.
(b) Stars are self-luminous and far-off bodies. They twinkle as a result of the atmospheric refraction of their light. When the light of stars enters the earth's atmosphere, it refracts many times and in random directions because of the varying optical densities of the different air layers of the atmosphere. Because of this random refraction, stars appear to move slightly, and we interpret this phenomenon as twinkling.
(c) The planets are large bodies and are very close to the earth. Therefore, the continuously changing atmosphere cannot cause much deviations in the light coming from the planets. The brightness of the planets remains the same, because of which they do not appear to twinkle at night.