Cepheid stars and RR Lyrae stars are variable because they pulsate in and out. The greater the luminosity of a Cepheid star, the longer its period of oscillation.
Variable stars have luminosities which increase and decrease with a regular period.
Main sequence stars have a nearly constant luminosity. By contrast, some giants and supergiants have luminosities which regularly increase and decrease. The two most interesting types of variable star are Cepheid variables and RR Lyrae variables. Cepheid variables are named after the star Delta Cephei, the fourth brightest star in the constellation Cepheus. The luminosity of Delta Cephei varies by a factor of two, with a period of 5 days.