The Mayans were so advanced in their astronomical math that they calculated really long periods of time. For example, they calculated the birth of the universe. In their Long Count calendar they had a unit called a Baktun which is about 394 years and starts at the birth of the universe as they knew it. The classic Mayan period lasted between the 8th and 9th Baktun. On Dec 21, 2012, the 13th Baktun ends and rolls over to the 14th Baktun. It's a New Baktun! We cannot pass up this chance to celebrate! It's also the Solstice which matches up with their calendar.
However, the plot thickens. Apparently there is something special to the Mayans about the end of the 13th Baktun. The way their calendar works is like an odometer. At the birth of the universe (according to Mayans), the calendar looked like 126.96.36.199.0. Since the numbers naturally roll over, on Dec 22, 2012, the Mayan date will be EXACTLY THE SAME AS THE BIRTH OF THE UNIVERSE. It will be, once again, 188.8.131.52.0. Of course, modern day calculations of the actual Big Bang are agreed to be about 13 billion years ago, not 5,125 years ago like the Mayans thought, heh. But their astronomy was very advanced for their time; the way they calculated big numbers is impressive compared even to today's calculation techniques. Sometimes I think that when we finally scorch the earth and millions of years have passed, enough for it to heal, some other civilization will rise up way smarter than us and laugh about how we couldn't even calculate the size of the universe correctly (or whatever).
In case you haven't seen it, NASA leaked their "day after the end of the world" video. This briefly explains some of the Mayan calendar logic.