Years / Epoch
The Jewish calendar uses the Anno Mundi epoch, Year of the World, counting from the year of creation, based on chronological data in the BIble. This is abbreviated to AM or A.M. According to Rabbinic tradition, the year 1 is not the year of creation, but one year before creation. The first day of the year is 1 Tishri 1 Anno Mundi, equivalent in the proleptic Julian calendar to 7 October 3761 BCE).
The Hebrew Year 5771 (year before the current year) began on 9 September 2010, and since it is a leap year, will end on 28 September 2011 (29 Elul).
19-Year Cycle (Metonic Cycle)
This is a cycle of 19 years, of which 12 are common years of 12 months, and 7 are leap years of 13 months.
The purpose of this system is to ensure that Passover always falls in Spring, as it is specifically designated as the Spring Festival. It also ensures that the Day of Atonement does not fall adjacent to a Sabbath.
Yom Kippur should not fall adjacent to Shabbat, because this would cause difficulties in coordinating the fast with Shabbat, and Hoshanah Rabbah should not fall on Saturday because it would interfere with the holiday's observances. So a day is added to the month of Cheshvan or subtracted from the month of Kislev of the previous year to prevent these things from happening. This process is sometimes referred to as "fixing" Rosh Hashanah. If you are interested in the details of how these calculations are performed, see Detailed Calendar Calculations.
I intend to add more detail concerning this topic of the Metonic Cycle and the topic of the Epoch briefly touched on above.