Cepheid variables are one particular type of variable star (one whose brightness changes with time) called after delta Cephei, the first star of this type to be observed.
These stars have a period of between one and fifty days and are giant yellow stars with a mass of between five and twenty times the mass of our Sun. Delta Cephei has a period of just under 5.4 days.
The luminosity of a Cepheid variable changes because the size of the star is changing. When the star is small its density is large and the temperature and pressure inside the star increase. This makes the star expand. When the star is large gravity causes it to contract again and the cycle repeats itself.