Variable stars show a change in their brightness over time.
This was very useful early in making distance measurements. We could see nearby stars and could find the relation between the time period of the light intensity variation an d the size of the star. When we then saw stars of the same time variation very far was as away we were able to know how bright these stars would have been if they were close. Using simple ideas about how li ght becomes dimmer with distance we then could calculate the distance. The stars light output varies because of the instability of the star as it burns fuel.