Around 120 BC, a Greek astronomer named Hipparchus created the first known catalogue of stars. While his star catalogue does not survive today, it is believed that he included around 850 stars. (This was later edited and increased to 1022 stars by Ptolemy in the second century AD and included in his famous work, the "Almagest.") Hipparchus listed the stars that could be seen in each constellation, described their positions, and rated their brightness on a scale of 1 to 6, the brightest being 1. This method of describing the brightness of a star survives today. Of course, Hipparchus had no telescope, and so could only see stars as dim as 6th magnitude, but today we can see stars with ground-based telescopes down to about 22nd magnitude.
As more accurate instruments came into play, astronomers found that each magnitude is about 2.5 times brighter than the next greater magnitude. This means that magnitude 1 stars are around 100 times brighter than magnitude 6. Also the more accurate measurements allowed the astronomers to assign stars decimal values, like 2.75, rather than rounding off to magnitude 2 or 3.
Today, there are stars known to be brighter than magnitude 1. For instance Vega (alpha Lyrae) has a visual magnitude of 0. Any other star brighter than Vega will have a negative value for its magnitude.
Usually, when an astronomer talks about magnitude, he means "apparemt magnitude," referring to the way we perceive stars, viewing them from Earth. Apparent magnitude is usually written with a lower case m, as in 3.24m. However, a stars brightness is not just a matter of how brightly it shines, but also how far away it is. For example, step outside at night and turn your porch light on, then walk to the end of the block. You'll see a difference in brightness, but the bulb hasn't changed. So, astronomers came up with another way to measure brightness and called this "absolute magnitude." Absoulte magnitude is defined as how bright a star would appear if it were exactly 10 parsecs (about 33 light years) away from Earth. For example, the Sun has an apparent magnitude of -26.7 (because it's very, very close) and an absolute magnitude of +4.8. Absolute magnitudes are often written with a capital M, as in 2.75M.