A star is called a variable star if its apparent brightness as seen from Earth changes over time. There are two basic types of variable stars: intrinsic variables, whose luminosity actually changes, and extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth. A star could be an intrinsic variable because it periodically swells and shrinks. A star could be an extrinsic variable because it has an orbiting companion that sometimes eclipses it.
Pulsating variable stars
There are many different types of pulsating variable stars. Some of them vary in brightness by as much as 100 times, and some have cycles that repeat as often as every few days, while others vary over months or years. In most cases these stars pulsate because they are at the end of their lives and have become unstable.
Eruptive variable stars
These stars are more likely to have very irregular cycles. They include protostars, which in the process of becoming main sequence stars, often have variations in their brightness. Giants and supergiants lose their matter relatively easily and may also experience eruptions. White dwarfs that are part of a binary system may also experience eruptions as they take matter from their companion star.
About half the visible stars are not isolated, they are part of multiple star systems. Pairs of stars that orbit each other are called binary stars or binaries. Observing how binaries orbit each other gives astronomers information about their masses.
Spectroscopy makes it possible to study binary star systems where the two stars are close together. Sometimes a binary system is so far from us, and the stars are so close together, that from Earth even with a telescope, we would only be able to see it as one star. Spectroscopy can tell astronomers the composition of the surface of a star, and if a star has absorption lines of elements that would normally not appear in a single star, they know that there are two different star types orbiting each other.
Some binary systems are oriented so that the two stars periodically eclipse each other when seen from Earth. In that case the apparent brightness of what appears to be a single star decreases when one star goes behind the other. Astronomers use photometry to measure changes in a star's brightness to study these systems.
Binary stars orbiting each other, and the corresponding changes in brightness over time. Image credit: LCO