The Precession of the Equinoxes refers to the gradual backwards movement (counter-zodiacal) of the stars relative to Earth's seasons.
This movement is caused by a very slow wobble in Earth's rotation. This shifting effect creates a gap between the Tropical Zodiac and the Sidereal Zodiac. So, for instance, the Vernal Equinox happens around March 20 or 21 each year, which is when the Sun appears to cross the Earth's equator going north. In the tropical zodiac, this corresponds to the Sun entering the sign of Aries.
However, because of precession, the Sun at tropical 0° Aries is no longer aligned with the constellation of Aries. Instead the Sun in the sidereal zodiac is around 5° Pisces at the vernal equinox.
It takes about 23,000 years for the Vernal Equinox to go full circle around the zodiac. The movement is approximately 1° every 72 years, which is roughly 2,000 years to per 30° sign.
The precession gap between Earth's seasons and the constellations is what creates the so-called Ages. The Age of Aquarius is probably the best known Age, thanks to the 1967 song
The astrological Age of Aquarius is assumed to begin around when the vernal equinox regresses all the way through Pisces and into Aquarius. However, it is a matter of much debate as to when that would happen. See Age of Aquarius for more.
Note: Precession of the equinoxes has nothing to do with planetary retrograde motion, which only applies to planets, not the whole zodiac.
Pronounced: Pre-SESH-un of the EE-quin-ox-ez.