2012, or to be specific, December 21, 2012 (the winter solstice), is the date on which the Mayan Long Count calender ends. Some say that world will end, or at least go about a great change.

Who were the Mayans?

The Mayans were people indigenous Mexico, Belize, El Salvador, and northwestern Honduras from 200 B.C.E. who were quite sophisticated for their time: they were advanced in agriculture, architecture, languages, and calenders. Their two calenders were even more accurate then our Gregorian calender today. First they created the Calender Round system, and later the Long Count system.

How did these calenders work?
The Calender Round system involved two overlapping annual cycles: the sacred 260 day cycle, and the secular 365 day cycle (which had 18 months with 20 days each, and 5 extra unlucky days at the end of the year). Each day was assigned a day number and day name for the sacred calender and a day number and month name for the secular calender. There were 52 years in a calender round, then it would start over. This system was bad at fixing events in a relationship with one another over long periods of time, so in 236 B.C.E. a priest created a new calender.
The Long Count system identified the date by counting forward from a previous date, in this case August 11th or 13th, 3114 B.C.E. The days were grouped into sets: baktun (144,000 days), k'atun (7,200 days), tun (360 days), uinal or winal (20 days), and kin (1 day). So a date that was 144,000 days from the start would be (1 baktun, 0 everything else). This calender cycled though one interval after another, and the interval was known as the Grand Cycle (13 baktuns, or 5,139 normal solar year). Some people think that the first grand cycle will end on December 21st 2012.
The Mayans believe that another interval will just start, and some Europeans and Americans believe it won't reset itself, and the world will end.

What else did the Mayans have to say about the end of the world?
On the final page of a text, called the Dresden Codex (about 1100 A.D.), there is a picture of an end-of-the-world scenario. The world is destroyed by a flood, a common prediction in ancient cultures (who probably experienced floods themselves). Anthony Aveni, an archaeoastronomer, said the scenario is not literal. Instead, it's supposed to a lesson about human behavior. And actually, the Mayans didn't even focus very much on predictions.

So, should we be worried?
No. Most scientists say that the probability of anything bad happening is unlikely. There are no unusual planetary alignments for 2012 and no giant solar storms that might disrupt satellite activity. For the probability of Earth being hit by meteors, comets or asteroids (like the one that wiped out the dinosaurs 65 million years ago), NASA astronomers are carrying out the Spaceguard Survey to find large asteroids near Earth. None as large as the one that killed the dinosaurs have been found. These discoveries are posted daily at the NASA NEO office website: http://neo.jpl.nasa.gov/

http://canteramaya.com/cantera_codex/wp-content/uploads/2010/10/dresden-codex1.jpg the Dresden Codex