What is a Variable?
Celestial variables include stars, galaxies and quasars. Quasars are really just galaxies with very bright cores. But by far most objects we can perceive with the unaided eye, binoculars or a small telescope are stars.
Most stars do not appear to change in a human lifetime, but a small fraction do. We call these "variable stars". A variable star is a star whose brightness changes as perceived from Earth.
A star's brightness is the intensity of light we measure from the star, the amount of energy per second we receive from it. That energy comes to us in the form of electromagnetic waves, or "light" that has traveled a great distance through space from the star to the Earth.
When we say "light", we usually mean the visible part of the electromagnetic spectrum. Visible light itself encompasses light of many different wavelengths or energies, corresponding to the colors of the rainbow (red, orange, yellow, green, blue, violet, etc.) that we see when white light is dispersed by the droplets in a cloud, or by a prism. But visible light is only a small part of the full electromagnetic spectrum.
When the intensity of light increases or decreases, we call it variability. In the case of variable stars, astronomers many years ago used the term variable to refer to the notion that the visible light observed from the star here on earth was changing in intensity.
A plot that shows the changes in intensity with time is called a light curve.