The 21st of December 2012 is the 'Winter' Solstice, when the Earth's position is tilted to it's extreme and the Tropic of Capricorn is the closest latitide to the sun.
This is the southern hemisphere's longest, day, and the northern hemisphere's shortest day.
Theories of the end of the world stemming from the Mayan Calendar are widespread. The reality is that the calendar does indeed end a long count period on this day, but not the end of the calendar completely, just as modern day calendars end on the 31st of December.