A falling star is not a star at all. It is not even part of a star. Stars do not fall. Our sun is a star. A falling star is a meteor.
Meteors are streaks of light in the sky.
The light is caused by a small speck of dust burning when it enters the earth's atmosphere. The dust comes from comets. These pieces of comet dust are called meteoroids. Most meteoroids are smaller than a grain of sand. The flash of light is called a meteor.