A falling star is a streak of light that is caused by small bits of rock and dust particles that are called meteoroids. They fall into the earth's atmosphere and burn up. This process leads to formation of meteors and if they survive the burning up, the remains hit the earth and are referred to as meteorites.
If you see a flash of light fall through the sky you may think that a star just fell. What really happened though is that a meteoroid just entered Earths atmosphere and burned up.
A falling star really isn't a star at all. It is actually a Meteoroids which are in reality parts of dust and rock and when they enter the earth's atmosphere, they burn up and leave a trail of light that looks like a falling or shooting star.