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The correlation constant links the day count to our common datesystem. It is the number of the julian day on which the long count (an Olmec and Mayan system for counting days) is all set to zero. This is day 4 - Flower or 4 - Ahau (Mayan). Even thought the Aztec presumably didn't use a long count, this correlation constant provides us with a standardized notation for linking the day count (and long count) to our common calendar.
Although most mesoamerican calendars use the same day count, they vary in the date of the New Year. The year constant provides a notation for linking the start of the year (xihuitl) to the day count. The constant is the number of the day in the year that occured on the day with a zero long count (hence, on the day with the correlation constant as its julian day number).
Mesoamerican calendars vary in their method for naming the year. Some calendars name the year after the first day of the year. Most calendars, as the Aztec calendar, name the year after the last day of the last month (meztli) of the year. This is the 360th day of the year, the one just before the 5 unlucky days. The day the gives its name to the year is called the year-bearer. Note that this date always occures twice a year.