What is a Sun Sign?
The Sun doesn't rise in exactly the same place every day. From our viewpoint here on Earth, it drifts over the course of a year. It's path through the sky is called the Ecliptic.
In ancient Babylon, the Ecliptic was divided into twelve equal pieces. Each piece was named after a major constellation, and the mythology of the Babylonians, and later the Greeks, defined the traits of those born under that constellation. This is the Zodiac, and is the center of astrology.
Carefully tracing the position of the sun will show that it moves through each of the twelve Zodiac signs over the course of the year. This is where the concept of astrological signs, or "Sun Signs," has it's start. A person's Sun Sign is tied to the constellation the Sun was traveling through at the moment of his birth.
The Sun is traditionally associated with will and individuality, so the Sun Sign covers the overall tendencies and direction a person has in their life. It covers such things as focus, determination, integrity, and ego. It describes general tendencies in an individual, like "Capricorns are gloomy" or Virgo is very orderly," as well as general predictions, like "Sagittarius should learn tact" and "Pisces should avoid alcohol and drug abuse”. This is also the element that shows how other people will treat this person, almost like a prediction of their "first impression."
This is only the starting point of Western Astrology, of course. The Sun Sign is only a very general description, and an astrological reading--a horoscope, or natal chart--takes the planets and Moon into account as well. For example, traditionally, Capricorns are very gloomy and depressed. This is a general trait ascribed to Capricorn, based on the position of the Sun. However, the positions of the other planets can counter--or sometimes enhance--this tendency. Complete horoscopes have to account for all of these elements, using the position of the sun as a starting point.