The earth, as everyone knows, rotates around its axis once every 24 hours, causing the cycles of night and day, and because the axis is not vertical but inclined, it also causes the seasons as the earth moves around the sun once a year. In addition to these two familiar motions, there is a third motion, caused by the torque produced by the gravity of the sun and moon (the lunisolar precession), and that produced by the gravitational influence of the other planets in the Solar System (the planetary precession). This torque causes the axis of the earth to very gradually precess, rotate very slowly much as the axis of a top that is tilted at an angle will also rotate. This precession occurs at a very slow rate, at 50.290966 seconds of arc every year, thus causing the axis to trace out a full circle against the fixed stars every 25,776 years, a period known as a Great Year. The phenomenon is said to have been discovered by the Greek astronomer Hipparchus in the 2nd century BC, who gave a figure of 46 seconds of arc per year.
This means that the axis of the earth gradually points to different stars (or empty space) in its precessional cycle. Today, the north star is Polaris, but in the time of the Sumerians it was the star Alpha Draconis (also known as Thuban), and 13,000 years from now it will point at Vega. The celestial coordinates of the stars also change due to this precession, and astronomers need to make calculations to determine what the sky looked like in the past and will look like in the future.
A specific (and apparently meaningful) change in celestial coordinates has to do with the constellations that are located in the ecliptic, or plane of the earth's orbit. These constellations are the zodiac, and every year at dawn during the vernal equinox a particular zodiac constellation is behind the sun when it rises. There are approximately 30 degrees in each constellation of the zodiac, so each such zodiac "age" lasts about 2160 years. Since about 60 BC up until about 2100 AD, the sun has been rising during the vernal equinox in the sign of Pisces, so we are living in the age of Pisces. Maybe it's just a coincidence that the dominant spiritual force during this present age is Christianity, whose first and most persistent symbol was not the cross but the fish, nor that Jesus called his disciples fishers of men. The fact that Jesus called himself the Lamb of God who would be sacrificed for the redemption of all might represent something other than a metaphor for the transition between the age of Aries and the age of Pisces that occurred during Jesus' lifetime. The age previous to this one, the age of Aries, lasted from 2220 BC to about 60 BC, and again I suppose it must be a coincidence that this was also the time when the cult of Amon-Ra became dominant in ancient Egypt, who was depicted with curled ram's horns (and whose temples were lined with ram-headed sphinxes), or that this was the time in ancient Judaism that animal sacrifices mainly of rams were made. The age before that one, from 4380 BC to 2220 BC was the age of Taurus, when again it must be a coincidence that this was when the bull-worshipping Minoan and Mycenean civilizations thrived, and the cults of Apis and Serapis, bull representations of Osiris, began to grow in Egypt. After 2100 AD, the sun will be seen rising in the sign of Aquarius, which is the New Age all of these hippies who believe in astrology keep talking about.
The change in age from Aries to Pisces that occurred at the beginning of the Christian era also makes all present-day astrological systems somewhat dubious. The sign of Aries is still given the time period of the vernal equinox, where it should be Pisces, meaning that to be correct with respect to what we actually see in the sky, all the dates for the signs need to be moved one house backward, meaning people who think their signs are Aries are really Pisces, the Pisceans are really born under the sign of Aquarius, the Aquarians are really Capricorn, and so forth. If you're familiar with the constellations and are lucky enough to witness a total solar eclipse happen on your birthday, the truth of this fact should be apparent on the moment of totality. The zodiac constellation behind the sun on your birthday will be the one before the one you think you were born under.
However, there also does seem to be a very real connection between the phenomenon of precession and global climate change, and it is theorized by some scientists that there is a connection between it and the cycles of ice ages that afflict the world from time to time. This is because the earth's orbit is not exactly circular, but is somewhat elliptical, so the earth is closer to and further from the sun at certain times of the year. The precession of the equinoxes determines at what point in the earth's orbit the seasons occur. So if we are at some point in the precessional cycle such that summer occurs when the earth is at aphelion (i.e. at its furthest from the sun), summers will likely be cooler, causing an overall drop in global temperatures, even more so when the earth's orbit is at its maximum eccentricity (i.e. the difference between perihelion and aphelion is at a maximum). This is an important component of the theory of the Milankovich cycle, which attempts to explain glaciation.
This phenomenon of precession is also observed on other planets. Mars, for instance, also precesses and has a Great Year of 175,000 years.