They are rocky and icy bodies left over from the formation of the solar system.
Meteors are tiny bits of dust that burn up in the Earth's upper atmosphere.
The population of comets and asteroids was much larger. With time, however, most of these bodies have either collided together to form the major planets, were ejected from the inner solar system into the Oort cloud, or were ejected out of the solar system altogether. The comets and asteroids we see today are the residual population.