It is a time period in the Mayan calender.

A b'ak'tun is a period of 144,000 days in the Mayan calendar.

The mayans had calanders one of which was called the longcount. something like every 1000 years (maybe a little bit less) the long count would go through a baktun which is like a year kind of. so 2012 will mark the end of the 13th baktun which is the end of the longcount calender. however it was people like the Spaniards then and the Americans now who said that since the calender is done it will be the end of days. but the mayans did not predict this. they have predictions for dates going as far as 4927A.D. so all in all it was not the mayans idea that the world would end but other cultures interpretation.

Well, the legend of the end of the world in 2012 is based on the Mayan calendar. According to this calendar, the date of the world's formation is 0 baktun 0 katun 0 tun and 0 winal (these are measurements of time), which is in our calendar 3114. August our 11 B.C, and it is over in 12 baktun 19 katun 19 tun and 17 winal, which is exactly on 2012. 20th of December. By this, the "end of the world" is on December 21. 2012., which is not the end of the world, but a start of another "world". The legend may strengthen by the date of this:

2012.20.12.(YYYY.DD.MM.)

No. The end of the world predictions for 2012 have no basis in reality. Many claim the Mayan long-count calendar predicts the ends of the world. It doesn't. It only marks the end of the 13 Baktun and the beginning of the 14. It is in the same sense that New Years will mark the end of 2012 and the beginning of 2013.