Magnitude
Astronomers use the magnitude system to quantify the brightness of celestial objects.
The higher the magnitude of an object, the fainter it appears. For example, Sirius has a magnitude of –1.46, while the brightest planet, Venus, can reach magnitude –4.9 at its brightest. The faintest stars visible to the unaided eye from a light-polluted town are around mag 3–4, while stars as faint as mag 6 can be seen from a truly dark site.
Colours of light
Magnitude values are often accompanied by a letter, such as U, B, or V, and often the same object may have multiple different magnitude values with different associated letters. These refer to the colour of light in which the star's brightness was measured, for example using a colored filter.
When no letter is specified, the magnitude may be assumed to be a visual, or V, magnitude. This refers to the brightness of the object as observed visually, by the human eye. A "B magnitude" refers to the brightness of the object when viewed through a blue filter. A very hot blue star might have a B magnitude which was much brighter than its V magnitude, whereas a cool red star, like Betelgeuse, would have a much fainter B magnitude.
In all colours of light, the star Vega is defined to have a magnitude of zero: this is the definition of the zero-point of the magnitude system, and the brightness of all objects is measured relative to Vega. In practice, this was not an ideal choice, since Vega is slightly variable, and so nowadays stars are usually measured relative to an idealised theoretical model of Vega. This model doesn't quite match the star itself, leaving Vega with a V magnitude of 0.03.
History
This system has a long history: it originated in an ancient Greek custom of dividing stars into six brightness categories. The brightest stars were referred to as being of first magnitude, a category which corresponded roughly to stars brighter than magnitude 1 today (about 13 stars). The next category were stars of second magnitude, roughly those brighter than magnitude 2 today (36 stars).
The final category, the sixth magnitude stars, included the very faintest stars visible to the unaided eye from the desert. In all, about 5000 stars are visible to the human eye from a very dark location.
However, making measurements of the brightnesses of stars remained a very inexact science until the advent of photography in the nineteenth century. Until that time, it relied entirely upon human observers making judgments of which stars were brighter or fainter than which other very similar stars.
With photographic plates, however, it became possible to quantify how fast the film darkened when exposed to the light of each star. This could be measured precisely, leading to two developments in the magnitude system.
First, it became possible to put the magnitude system on a formal mathematical footing. In 1856, the English astronomer Norman Robert Pogson defined the precise difference in the brightness of stars of each magnitude. He proposed that a difference of five magnitudes should correspond to a difference in brightness of 100 times. He found that this very closely matched historical magnitude measurements.
Thus, a star of magnitude 6 is a hundred times fainter than a star of mag 1. Equivalently, a star of mag 3.5 is ten times fainter than a star of mag 1, since a difference of 2.5 magnitudes corresponds to a factor of ten in brightness.
The second development stemmed from the observation that the relative brightness of stars as recorded on photographic plates did not always match their relative brightness as perceived by the human eye. It was realised that photographic plates were much more sensitive to blue light than the human eye, and less responsive to red light. This demonstrated the need to prefix magnitude measurements with letters indicating which colours of light had been collected when the star's brightness was measured.
Initially, two letters were used: B (blue; photographic), and V (visual). To these was later added U (ultraviolet) to complete the "UBV photometric system", which was formalised in the 1950s by American astronomers Harold Johnson and William Morgan. Precise definitions were formalised, stating which wavelengths of light were to be admitted by each filter.
To these letters, the South African astronomer Alan Cousins later added R (red) and I (infrared). Since then, the range of letters used has continued to grow. Among the most recently created filters you may see quoted on In-The-Sky.org are BP and RP, referring specifically to the blue and red filters used on the Gaia space observatory.