I don't believe in astrology; I'm a Sagittarius and we're skeptical. - Arthur C. Clarke
People's sign, or sun sign, is determined by which zodiacal constellation the sun was in when they were born. If it seems confusing to think of the sun being in a constellation at any time, think of the stars and planets that are visible from Earth as if they exist on a giant sphere that encompasses our planet. This is known as the celestial sphere, and it is used by astrologers and astronomers alike to make measurements of the things we see in the night sky.
As the Earth revolves around the sun, the sun appears to move across the Celestial Sphere, following a path known as the ecliptic. Each day, the sun moves about 1 degree along the ecliptic, which is offset from the Earth's axis of rotation by 23.5 degrees. This degree variation is what accounts for seasonal changes in the amount of sunlight the Earth receives.
Depending on the time of the year and the specific astrological system used, the sun will have a certain sign as its backdrop in the daytime sky. Ancient astrologers figured this out by watching which sign rose first at night and set last in the morning.
Therefore, when someone says, "I'm a Leo," that means that the sun was in the constellation Leo on the day that person was born.
Many astrologers divide the ecliptic into 12 equal regions and assign zodiacal names to each division, although the divisions don't necessarily line up with the appropriate constellation. This is known as the sidereal zodiac, and was actually developed around 400 B.C. Other astrologers use the tropical zodiac, in which the position of the signs are linked to the seasons. Because of the Earth's precession (basically, the Earth "wobbles" slightly on its axis as it rotates -- see What is the Chandler wobble? to learn more), the two methods don't really match up any more. They did about 2,000 years ago, but now the constellations have shifted considerably in the sky (Campion, pg. 11).
In the next section, we'll take a look at each sign of the zodiac and the traits associated with it.