A few years ago, I was in a synagogue, and I overheard one man ask another, "When is Chanukkah this year?" The other man smiled slyly and replied, "Same as always: the 25th of Kislev." This humorous comment makes an important point: the date of Jewish holidays does not change from year to year. Holidays are celebrated on the same day of the Jewish calendar every year, but the Jewish year is not the same length as a solar year on the Gregorian calendar used by most of the western world, so the date shifts on the Gregorian calendar.
Background and History

The Jewish calendar is primarily lunar, with each month beginning on the new moon, when the first sliver of moon becomes visible after the dark of the moon. In ancient times, the new months used to be determined by observation. When people observed the new moon, they would notify the Sanhedrin. When the Sanhedrin heard testimony from two independent, reliable eyewitnesses that the new moon occurred on a certain date, they would declare the rosh chodesh (first of the month) and send out messengers to tell people when the month began.

The problem with strictly lunar calendars is that there are approximately 12.4 lunar months in every solar year, so a 12-month lunar calendar loses about 11 days every year and a 13-month lunar gains about 19 days every year. The months on such a calendar "drift" relative to the solar year. On a 12 month calendar, the month of Nissan, which is supposed to occur in the Spring, occurs 11 days earlier each year, eventually occurring in the Winter, the Fall, the Summer, and then the Spring again. To compensate for this drift, an extra month was occasionally added: a second month of Adar. The month of Nissan would occur 11 days earlier for two or three years, and then would jump forward 29 or 30 days, balancing out the drift.

In the fourth century, Hillel II established a fixed calendar based on mathematical and astronomical calculations. This calendar, still in use, standardized the length of months and the addition of months over the course of a 19 year cycle, so that the lunar calendar realigns with the solar years. Adar II is added in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the cycle. The current cycle began in Jewish year 5758 (the year that began October 2, 1997).

In addition, Yom Kippur should not fall adjacent to Shabbat, because this would cause difficulties in coordinating the fast with Shabbat, and Hoshanah Rabba should not fall on Saturday because it would interfere with the holiday's observances. 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.