Each world age lasts "13 Baktuns" (ca. 5125.36 solar years) in their "time calculating system" which was based upon astronomical events and cycles that were somewhat significant to the Mayans. According to their Long Count calendar, we are approaching the end of the "Fifth Sun", or the 5th world age, which they believed to come with important changes on "The Earth Element" (geological events that cause catastrophes like earthquakes, volcanic eruptions etc.)
They did not mention "the end of the world" but they prophesied a radical change on the way human societies live on this planet, with the beginning of a new world age, "The Sixth Sun".
(We must keep in mind that the calendar system was not entirely "invented" by the Mayans; it was a "heritage" that they acquired from much older Mesoamerican cultures which they developed and fine tuned in centuries.)
Back in the fifties, Mayan long count dates were converted to our Gregorian calendars by a bunch of scholars (known as the "GMT Solution", by the initials of the scientists who worked on the Calendar.) According to this solution, the beginning date of the 5th Sun was August 12, 3114 BCE, while the "end date" was December 22, 2012 CE (simply the Winter Solstice of 2012.)
The beginning date is somewhat intriguing: Almost all the first known civilizations around the world that created hierarchically organized city-states and a central government, flourished about the year 3100 BCE. In other words, beginning of the "5th Sun" appears like the beginning of our "written history".