The are used as standard candles to measure distances within our galaxy and nearby galaxies. That is the importance of cepheid variables.
What are Cepheid Variables ? In 1784 John Goodricke discovered that the fourth brightest star in the Cepheus constellation, ##delta##-Cephei’s magnitude varied periodically. Later it was found that there are many different class of variable stars and ##delta##-Cephei is just one among the variable star of its kind. It became the prototype for the class of variable stars it belongs too. All variable stars belonging to this class are called Cepheid Variables.
What are standard candles? The distance to a star can be determined if we know its intrinsic brightness (absolute magnitude) and its brightness as seen from here on Earth (apparent magnitude). We can only measure the apparent magnitude of a celestial object from Earth. If there is a way of finding its absolute magnitude then we can find the distance to that object.
Fortunately there are classes of celestial objects which all have the same intrinsic brightness which is known. Such objects are called Standard Candles because they help us to measure distances to that part of the space where they are located.
Why are the cepheid variables used as standard candles? In 1912 Henrietta Swan Leavitt discovered that the period of brightness oscillations of the cepheid variable stars were tightly correlated to their intrinsic brightness and found a relation connecting the two quantities.
This enabled astronomers to determine the intrinsic brightness of a cepheid variable just by measuring its brightness oscillation period making its possible to measure distances that are farther away than the limits of the method of parallax of measuring distances. For the first time it allowed astronomers to estimate the distance to nearby galaxies.
It is using the Cepheid Variables that Edwin Hubble was able to show that the Andromeda Spiral Nebula lies outside the Milkyway Galaxy.