The calendar associated with predicting the end of the world in 2012 was the Mayan calendar. More precisely, the claim centered on the Maya Long Count calendar and the completion of a major cycle on December 21, 2012.
The Long Count was designed to record long spans of time using units such as baktuns. The 2012 date marked the end of the 13th baktun, a cycle lasting roughly 5,126 years. Popular books, documentaries, and internet theories transformed that calendrical transition into predictions of planetary destruction.
That interpretation was not supported by Maya evidence. Maya scholars generally explain that the date marked the end of one cycle and the beginning of another, not the end of creation or civilization. In fact, surviving Maya inscriptions refer to dates far beyond 2012. The film 2012 used the popular doomsday interpretation as part of its disaster-fiction plot, which helped keep the misconception in public memory.