The absolute magnitude of a Cepheid variable can be deduced from its period (the interval between times maximum brightness), which is easily measured. Once you know the absolute brightness (how much power is emitted) of a star, its distance can easily be inferred from the apparent magnitude.
The mechanism whereby the period of Cepheid variables is related to the absolute brightness (and mass) was first explained by Robert Christy, a Caltech physics professor who worked on the Manhattan (atomic bomb) Project. Prof. Christy passed away last year. He was one of my physics profs there.
RR Lyrae variables have a similar period-luminosity correlation, as do Cepheids, but the starts are smaller and cooler, and the mechanism of both involves pulsation (periodic radius and temperture variation).
You can read more about this type varable at
http://en.wikipedia.org/wiki/RR_Lyrae_variable
Again, once you know how bright a star really is, its apparent brightness can be used to determine the distance. Both types are sometimes referred to as "standard candles"
How are cepheid and rr lyrae variables used in determining distances?
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