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Cepheid variables provide a critical rung on the cosmic distance scale ladder. Using parallax, we can only determine the distances to a few thousand of the nearest stars. Some of these stars are Cepheids. Cepheids are pulsating stars, they oscillate in intrinsic brightness with a period that is proportional to their average brightness. So, by measuring the period of oscillation, you can determine its intrinsic brightness. You can also measure its apparent brightness; the difference between them tells you the distance to the Cepheid.

Cepheids are very luminous stars, so they can be seen at great distances, even in other galaxies! In fact, the Hubble Space Telescope Key Project was to determine Cepheid distances to 18 galaxies. The goal was to calibrate the last rung on the cosmic distance scale ladder: Hubble's law. The calibrated law allows us to determine the distance to virtually any object in the Universe to an accuracy of 10 percent (modulo cosmological effects).

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