"Hey, the constellations don't line up anymore!"
When the ancient Babylonians first started tracking the motions of the heavens, they divided the sky into 30 degree increments and gave each section over to the rule of a constellation. This is the Zodiac, the band of the sky that all of the heavenly bodies move through. It's a strip of sky about seven degrees across. But they didn't count on precession.
The Earth is slightly tilted on it's axis. Because of this, the constellations don't stay in the same place. Over time, the North Pole slowly points to a different star, and as this happens, the circle of the Zodiac slowly spins around the planet.
In a nutshell, the constellations move, but astrology doesn't. Astrologers measure the sky based on their positions on the Vernal Equinox, and not by what stars are actually in the sky. So, they might say "the Sun was in Aries when you were born," knowing full well that the sun was really in Pisces.
This has caused quite a stir in the astrology community. On one side, you have the astrologers who have adjusted theircharts to account for the drifting constellations. Some of them have even corrected an ancient mistake and added a thirteenth sign, Ophiuchus, to their Zodiac, who shares his slice of the sky with Scorpio. These astrologers follow what's called a Sidereal system, focusing on the positions of the stars themselves.
On the other side, you have the Tropical astrologers. They believe that the constellations are irrelevant, because they were merely place-holders or handy symbols that were used to mark the divisions in the original system. Their view is that the horoscope is designed to measure the influence of the planets in regards to earth, and not the influence of the stars behind the planets. The horoscope is built from the Vernal Equinox, after all, and not from one of the stars in Aries.