Very similar to the Mayan Calendar. The Aztecs didn't add much to the system except treating it even more seriously regarding sacrifices to the Gods.

The two systems are:
  • The 13/20 day naming system that repeats itself every 260 days
  • The 18 months of 20 days each system that with an additional 5 unlucky days to make up the year
Every 52 years the systems synchronize, and the calendar starts over which made the Aztecs go absolutely crazy sacrificing to make sure that the sun would rise again the first day of a new period. Cortes and his troops found 132,000 skulls under the main temple of Tenochtitlan when tearing down the main temple of the city.

The system was also one of the reasons for the easy downfall of the Aztec Empire: Just as Cortes entered the city - November 8, 1519 - , the periods were turning - and an old legend had it that a god (and old king) - Quetzacoatl - would return that excact year. Rumour has it that Cortes knew this (from his mistress Malinche) and dressed a bit up for it.