A variable star is a star that is sometimes brighter or dimmer. Most stars have only very small differences in brightness, like the Sun; but some stars can vary hugely.
There are generally two types of variable stars:
A star being eclipsed, where the changes in brightness are from perspective, are called extrinsic variables. For example, in a solar eclipse the moon gets between the sun and Earth. Some binary star systems sometimes show eclipses, as do planetary systems with high-mass planets such as gas giants.
Stars whose brightness actually changes are called intrinsic variables. These stars appear to get bigger and smaller over time. Some pulsate at a constant rate, some do not. All of them change the rate at which energy is put out, which changes their appearance to us.