Basically, there are three calendars ! Two of them, the tzolkin (ritual and agricultural) and the Haab (solar) are used together and are known as the 'calendar round'. The 'long count' calendar, is a long term calendar, spanning thousands of years and is the one that has been interpreted as signaling the end of the world on end-date December 21st, 2012 !
The Mayan understanding of mathematics and the cosmos is breathtaking and you would think it was beyond the comprehension of anyone from that era. Their skill is recognized through the accuracy of the calendars over long periods of time. They are complex and intricate, but here's the basics.
The tzolkin has 260 days ( a kin being one day). The belief is, that this relates to the maize growing cycle and/or the length of pregnancy and/or the length of time the sun is directly overhead at Izapa - the place of it's creation. It is used in conjunction with the Haab, the solar calendar of 365 days with which we are familiar. The complete calendar was capable of a 52 year cycle and is still used in some parts of Guatemala today.
The long count calendar, with end date December 21st 2012, uses a long cycle of nearly 26,000 years ! This is split into five great cycles of around 5,125 years. It's start date has been correlated to our calendar as 13th August, 3114 B.C.E.
We are currently in the last days of the last cycle and will be the first humans in living history to witness it ! Cosmologically, this is highly significant, as our planet, the solar system and the sun will be in alignment with the centre of our galaxy. 2000 years ago, the Mayans new this and predicted it exactly ! ( see cosmology )
The 'end of the world' theory is simply the ending of the calendar and the end of the cycle. It was written twenty centuries before it's conclusion, so there would be no need to continue and had they been around today, they may well do what you and I would do when our calendar is nearly finished - get another one ready !