While the secular (also referred to as Gregorian) calendar is based on the earth's rotation around the sun, the Hebrew calendar calculates months according to the moon and years according to the sun.
Each new Jewish month begins and ends with the appearance of the new moon. Months of the Hebrew calendar are: Nisan, Iyar, Sivan, Tammuz, Av, Elul, Tishrei, Cheshvan, Kislev, Tevet, Shevat, Adar.
The 12 months of the Jewish calendar contain 354 days. The shortfall of 11 days from the 365 secular calendar is made up by adding a thirteenth month every few years.
Seven out of every nineteen years (years 3, 6, 8, 11, 14, 17 and 19) has an added month. The added month is called Adar Bet. The Jewish leap year ensures that the holidays occur during the same season each year (High Holiays in the autumn, Chanukah in the winter, Purim and Passover in the Spring, ...).
In the year 358, Hillel II instituted the leap year system and the Hebrew calendar used today. The names currently used for the months first appeared during the Babylonian exile and are either Akkadian, Assyrian or Babylonian in origin. In the Bible, the months are generally referred to as the first month, the second month, .... In the oldest known Hebrew calendar, the tenth-century BCE Gezer calendar, the months are based on the agricultural cycle.
The Jewish year is calculated by adding 3760 to the civil year. 3760 was calculated by adding up the ages of people in the Bible back to the time of creation. However, this does not necessarily mean that the universe was created less than 6000 years ago as the definition of "years" has not been a constant throughout history.
Instead of using the terms B.C. and A.D. (which focus on the birth of Jesus), Jews use the terms B.C.E. (before the common era) and C.E. (common era).