Nobody really knows, but there are plenty of people willing to sell their take on it; anything from nothing happening at all to God hitting the Universe's reset button.
The whole hullabaloo stems from the Mayan calendar's Long Count. It's based on cycles derived from the precession of the equinoxes, astronomical alignments, and Mayan mythology.
The Long Count is a mixed base 20/base 18 representation of the number of days since the beginning of the "Mayan Era" and creation of the Fifth World. The starting point roughly corresponds to August 13th, 3114 BC.
Dates are written in the form: baktun.katun.tun.unial.kin
1 kin is one day.
An unial is 20 kin.
A tun is 18 unial, 360 days.
A katun is 20 tun, 7200 days, almost 20 years.
One baktun is 20 katun, or about 394 years.
April 4th is 12.19.14.3.12 by Long Count reckoning.
In theory, the system can readily be extended to delineate any length of time, by simply adding higher-order units. In practice, Long Count inscriptions confine themselves to only five units, since this was adequate to express any historical or current date within human experience. Even so, inscriptions exist which noted even larger units.
The much discussed 13-baktun cycle is completed 1,872,000 days after 0.0.0.0.0. This period of time is the "Great Cycle" of the Long Count and equals 5125.36 years. Interestingly, this is almost exactly one-fifth of the time required for the Earth to complete one cycle of precession of the equinoxes. Most ancient societies that paid much mind to the heavens would notice precession after three or four generations. The Mayans were believed to be aware of this phenomenon.
So what's so special about 13.0.0.0.0?
It falls on or about December 21st, 2012. On this day, at the winter solstice, from our point of view on Earth, the Sun will occupy the point in the sky where the plane of the ecliptic precisely intersects the central plane of our Milky Way Galaxy.
In this part of the sky, a vast interstellar dust cloud in the general direction of the galactic center obscures much of the Milky Way. The Mayans visualized this particular section of the Milky Way as a celestial manifestation of the Sacred Tree, the center of the entire corpus of Mayan Creation myths, the source of life and the path to both the heavens and the underworld. The crossing point of Milky Way and ecliptic is the doorway.
Pacal, a semi-mythological god-king of Palenque, was equated with the sun, and he is portrayed "entering" the Sacred Tree on the day the sun conjuncts the crossing point of ecliptic and Milky Way. This is the only date when the Sun/Pacal could jump from the ecliptic track and travel the Milky Way up and around the vault of heaven and enter the "Heart of Sky," the unmarked polar "dark region" symbolizing death and the underworld around which everything was observed to revolve. Life revolves around death - a characteristically Mayan belief. The dates on which the sun conjuncts the "Sacred Tree" are thus very important.
Early skywatchers of the Mayan Classical era (circa 355 BC) would then observe the sun to conjunct the Sacred Tree of the Milky Way on or around November 18th. Over a relatively short period of time, as an awareness of precession was emerging, this date was seen to slowly approach winter solstice, a critical date in its own right in early Mayan cosmo-conception. At this point, the rate of precession was calculated, the Long Count was perfected and inaugurated with a starting date far enough in the past to accommodate the Mayan creation mythos, and the appropriate winter solstice date in 2012 AD was set as the end of a Great Cycle. This was by no means seen as the end of the world, but the completion of a grand era and the beginning of a new age.
Essentially, the whole 12/12/2012 thing is the Mayan equivalent of Y2K. And we all know how much fuss that caused.