If it were possible to see the stars in daylight, the Sun would currently appear to be in the constellation Gemini. But, in six months' time, when the Earth has completed half of its solar circuit, it will be in the opposite half of the sky, in the constellation Sagittarius.
The apparent path that the Sun traces out in the sky is called the ecliptic. On its annual journey along the ecliptic the Sun passes across a number of constellations, collectively known as the zodiac (derived from the Greek zodiakos kyklos, meaning "circle of animals", because many of its constellations represent beasts: Taurus the bull, Cancer the crab, Aries the ram, and so on).
Ancient astrologers mapped out the location of the Sun on the zodiac throughout the year, and conferred the title House of the Sun on one constellation each month, giving each period its own "sign of the zodiac", or Sun sign. These signs and dates are still used by astrologers today.
Things have changed since those early astrologers performed their calculations, however. The gravitational pull of the Sun and Moon causes the Earth to wobble as it spins (a phenomenon known as precession). This happens very slowly - one wobble every 25,000 years or so. But in the time since Sun signs were first calculated, precession has shifted the constellations eastward across our sky. So the astrological signs that appear in daily horoscopes are not based on the position of the Sun in 2006, they are based on the position of the Sun in 450bc. The astrological calendar is thousands of years out-of-date. When zodiacal charts were first drawn up, the Sun was in the constellation Capricornus each January 1.
That's why someone born on January 1 will recognise themselves as "a Capricorn", despite the fact that the Sun now lies in Sagittarius at the time of each New Year. In addition, the ecliptic actually passes through 13 constellations, rather than the traditional 12. Each year, the Sun spends more than two weeks in the constellation Ophiuchus, the serpent-bearer.
Ophiuchus never made it into the zodiac, possibly for superstitious reasons. However, strictly speaking, anyone born between November 30 and December 17 ought to be considered "an Ophiuchan" - in fact, most Sagittarians should really be known as Ophiuchans.