Vox provides a very clear explanation of Henrietta Leavitt's 1908 discovery that allows us to estimate the distance to stars and galaxies.
The book Einstein's Greatest Mistake (which I previously reviewed here) also discusses Leavitt's contributions (pages 137-142). This section of the book explains why stars differ in their degree of pulsation: "We're used to our sun shining pretty evenly, at just about the same intensity day after day. But that's because the layers of fuel in the sun burn fairly evenly. In some very different stars, the burning is highly uneven" (pp. 138-139). The latter type of stars alternate between states of hot, bright, expansion and, after the expansion releases pressure, a dimmed and slimmed down appearance.