The Mayan, like many other ancient civilizations, were proficient in the science of Astronomy, which helps in determining a calendar. They were able to measure what we now call Precession, which is the slow wobble of the Earth. In addition to spinning around once on its axis in a day, and revolving around the Sun in a year, the Earth wobbles like a gigantic top, one wobble taking 26,000 years to complete. Their calendar simply noted when the ending of one wobble occurs and the beginning of another wobble begins.
The calendar doesn't really end; it, like a car's odometer, merely reaches the end of its cycle and starts over, or like our calendar transitions from December to January at the conclusion of an Earth revolution.
It's not the End of the World; it's the end of the calendar.