The Aztec calendar came about as a result of the Aztec people's need to make an unpredictable world more predictable. The Aztec people had observed that everything occurred in cycles; over a period of time, things repeated themselves and they needed a way to predict when this would take place. The Aztecs had two very important aspects of their daily lifes that they need to make predictable and the calendar they developed is a two part calendar that includes both.
The first aspect that needed to be predicted was agricultrural. When crops could be planted, how long before they could be harvested, when could heavy rains and flooding be expected, when animals would mate and bear young, and when the moon would be full or dark. Through repeated observations of the world and sky around them, these cycles became clear and the Aztecs developed the xuipohualli or "year count" calendar which was based on the astronomical cycle of the earth traveling around the sun.
This calendar was originally made up of 18 groups (months) of 20 days with 5 extra days to make a total of 365. The last 5 left over days were called nemontemi "those who are there" and were considered to be bad luck days. Over a period of time they discovered that the calendar was slowly shifting and they added an additional day every 4 years to prevent the chift and restore their calendar to an accurate count of the days of the year.
The second important aspect of Aztec life was religious. The Aztec pantheon included approximately 100 different gods. Appeasing and honoring these gods was a part of their daily lives and it was very important that religious ceremonies were conducted at the proper time and order. Failure to do so would bring disaster on the Aztec people. The priests devised a 2nd calendar to address this important issue. This calendar was called tonalpohualli, the "day count" calendar. This calendar was based on 20 groups (months) of 13 days each making a religious year 260 days long. This calendar was also used to calculate their centuries which were actually 52 years long. At the end of each century, the Aztecs celebrated a festival called the Binding Up Of Years (New Fire Ceremony). All fires and lights were extinguished and for 12 days the people fasted and prayed. On the last day, as the "star of fire reached it's zenith", the priests made a human sacrifice and then lit a new fire. This fire was then used to light all of the fires in the city signifying a start to the new century.
Since Aztec writing was based on pictographs, these were incorporated into the calendars. There were 20 primary characters used to show the days in the xuipohualli and months in the tonalpohualli. These pictographs were:
The Aztec belief that everything occured in cycles made the circle a "sacred symbol". The Aztecs incorporated this into their depiction of the Aztec calendar. The Aztec calendar became a circle with concentric rings containing the pictographs which designated the different days and months of both calendars in one large round. Early Aztec calendars were drawn, painted, engraved, or carved onto various materials. Every temple and village had a copy; but, these were destructible and as important as the calendar was to the Aztecs; a permanent version was needed. Then, if a calendar was destroyed, a new calendar could be commissioned based on the permanent one. This prevented errors from being accidentally introduced. The Aztec calendar that we are most aware of is this permanent version. It is a 12 ft round slab of stone 3 ft thick and it weighs approximately 25 tons. It currently is on display in Mexico's National Museaum of Archeology and History. It has definately proven it's permanence.
The Aztec calendar is still in use today and there are websites where you can go to find out what the current date is according to the Aztec calendar and even which date corresponds to your birthdate.