Contrary to some fanciful speculation, it will not be the end of the world. It will only be the end of a Mayan Long Count, after which a new one starts. On 12/22, most of us will wake up, and go back to our Christmas shopping. On the other hand, some people will die on 12/21, but that will be merely the natural course of events, and have nothing to do with Mayan astronomy.
Due to precession, the wobble in the earth's spin, the apparent position of the sun (observed from earth, with respect to the stars) at the solstices and equinoxes is slowly moving along the ecliptic, which is the apparent path the sun takes through the sky (and through the constellations known as the Zodiac) every year. Each of the solstice and equinox points takes 26,000 years to move one complete cycle around the ecliptic, this movement being in the opposite direction of the sun's yearly path. Thus, while the sun moves from Aries to Taurus to Gemini, each point will slowly move from Gemini to Taurus to Aries at some time within the 26,000-year cycle. As this article by John Major Jenkins explains, the winter solstice point is close to the galactic equator. For more information, go to his website.