Brightness and Magnitude
We see stars in a large range of brightness, from as bright as the brightest star Sirius (apart from the Sun of course) until the faintest stars just visible with the naked eye. Beyond that we can see even fainter stars with binoculars or telescopes.
Brightness is no measure for distance to the star.
A very faint star could indeed be relatively near by, but just be less luminous than other stars. Bright stars could be far away when they have a very great luminosity.
Arctures has an apparent magnitude of -0.05 and Proxima Centauri has an apparent magnitude of 11.01. Does this mean that Arcturus is closer to us?
Not at all. Arctures is ten times further away than Proxima Centauri.
Brightness as we see it, i.e. apparent brightness, is usually measured on a magnitude scale. The magnitude of a star, planet or other celestial body is a measure of its apparent brightness as seen by an observer on Earth.
The brighter the object appears, the lower the numerical value of its magnitude.
Ancient Greek astronomers divided stars visible to the naked eye into six magnitudes. Later this system was formalised into a system that defines a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star.
Vega is used as the standard reference star and has magnitude 0 (zero). The modern system is no longer limited to 6 magnitudes or only to visible light. Very bright objects have a negative magnitude.
Sirius, the brightest star of the celestial sphere, has a magnitude of −1.46. The modern scale includes the Moon and the Sun; the full Moon has a magnitude of −12.6 and the Sun has a magnitude of −26.73.
The faintest stars that are observable by the naked eye have a magnitude of 6. The Hubble Space Telescope has located stars as faint as magnitude of 30 at visible wavelengths.
Absolute magnitude uses the same scale but measures the actual brightness (usually called luminosity) of a star. Without additional information, we cannot tell what the absolute magnitude of a star is. Astronomers can calculate the distance to a star when they know both the apparent and absolute magnitude. See our separate Ebook "Stellar Distance" for more details.