Diagram of the different types of variable stars. http://www.atnf.csiro.au/outreach/education/senior/astrophysics/variable_types.html
Variable stars are stars that, as seen from earth, have varying levels of brightness. There is a huge amount of different types of variable stars, and their brightnesses fluctuate for many different reasons. The definite relationship between the period of the pulsations and the luminosity can help astronomers to determine the distance to these stars.
T-Tauri: T-Tauri stars are young stars that just started burning hydrogen in their cores. These stars have intense flares and eruptions on their surface, which causes irregular light to be emitted.
Cepheid: Cepheid stars are a very broad category of variable stars. These stars are unstable due to their drained hydrogen fuel supply, and therefore they pulsate. These pulsations can be used by astronomers to determine distance.
RR Lyrae: RR Lyrae stars periodically grow larger and smaller, similarly to a balloon, which causes a change in its perceived brightness from earth.
A part of a galaxy called M33. 6 photos taken over 2 years which shows the varying levels of brightness from the variable stars in the galaxy. http://www.astro.princeton.edu/~jhartman/M33_Movies_new.html
A Mira variable star with changing brightness, as seen from a telescope. http://www.virtualtelescope.eu/history/