A Cepheid is an intrinsically variable star with a period of 1-70 days. Light curves of Cepheids reveal that they undergo a rapid rise in brightness and then a more gradual decline.
The period-luminosity relation was discovered by Henrietta Leavitt in the 1900s. She studied the variable stars in the Large and Small Magellanic Clouds. The stars with longer periods were brighter than the stars with shorter periods. Since all the stars were at approximately the same relatively distance from us on earth, she determined that more luminous Cepheids pulsated more slowly.
Type I Cepheids, or classical Cepheids are about four times more luminous than Type II Cepheids. They follow the following pattern: the longer the period, the more luminous it is.
Type II Cepheids, or W Virginis Cepheids, are less luminous than Type I Cepheids. They are older than Type I Cepheids. The decline side of their light curves have a characteristic bump.