This article is from the Calendars FAQ, by Claus Tondering email@example.com with numerous contributions by others.
(I am very grateful to Chris Carrier for providing most of the
information about the Maya calendar.)
Among their other accomplishments, the ancient Mayas invented a
calendar of remarkable accuracy and complexity. The Maya calendar was
adopted by the other Mesoamerican nations, such as the Aztecs and the
Toltec, which adopted the mechanics of the calendar unaltered but
changed the names of the days of the week and the months.
The Maya calendar uses three different dating systems in parallel, the
"Long Count", the "Tzolkin" (divine calendar), and the "Haab" (civil
calendar). Of these, only the Haab has a direct relationship to the
length of the year.
A typical Mayan date looks like this: 184.108.40.206.6, 3 Cimi 4 Zotz.
220.127.116.11.6 is the Long Count date.
3 Cimi is the Tzolkin date.
4 Zotz is the Haab date.