Cepheids are a class of stars whose absolute magnitude (luminosity) tallies extremely closely with their period of varibility. Knowing this period, astronomers can compare the star's absolute magnitude with its observed magnitude, and determine quite accurately its distance from Earth .
The relationship between periodicity and luminosity was discovered and then experimentally verified using the parallax method for close-by Cepheids.
Cepheid variables were observed in the Andromeda Galaxy by Edwin Hubble in the early 1920s, proving conclusively that Andromeda is far too distant to be part of our Milky Way . This was the first indication that the universe extends beyond our own galaxy. Later observations of the red shift of more distant galaxies showed that the universe is expanding, providing the first empirical evidence for the Big Bang theory.