I’m a non-observant Jew, but I’ve still been forced to play the role of cultural ambassador to my gentile friends. 
Now, I’ve been asked this question a few times, and my only though is that since the lunar calendar doesn’t match up with the Gregorian calendar, the date Chanukah falls upon varies. However, I would be remiss if I was a member of the SD community and still chose to offer this lackluster explanation.
Help?
Shalom! ;j
Hanukah is on the 25th day of the Hebrew month of Kislev. The difference in dates is because of the calendar differences.
How to th dates in a lunar calendar change from year to year? By that, I mean, why is the 25th day of Kislev so different on the Gregorian calendar on one year than on another? I assume both calendars are 365 days because the dates of the Jewish holidays stay roughly in the same position relative to the solstice. Is that assumption correct? If not, and the number of days in a lunar calendar is different, why then doesn’t Chanukah (and any other holiday on a lunal calendar) move steadily earlier or later every year?
–Cliffy
No, the Hebrew calendar varies between 353 and 385 days, depending on whether it’s a leap year or not.
After reading that page, you’ll probably be sorry you asked…
The solar and lunar calendars don’t match up. There are fewer days in a lunar month, so every so often, there is an additional month thrown into the lunar year to keep things more or less even with the seasons.
Robin
Here’s a link that can explain it better than I.
Basically the Jews use a lunar calendar that is adjusted by leap months to more or less coincide with the solar year. This is becuase the festivals - passover, shavuot, and sukkot - are agricultural festivals (planting and harvesting) that are based on a solar year. Note the Muslim calendar is strictly a lunar calendar so Ramadan is progresses (regresses?) through the solar year. My WAG is that there are no seasonallly dependent events in Islam that require the tie in to a solar year.
Why the hebrews did not use a solar calendar? IMHO - i don’t know.
BTW - the Jewish day starts at sunset.
“Bachelorette number 1, If you were going to spin my dreidel, how long could you keep it up?” ;j
On the contrary… Mohammed explicitly forbade the practice of adding extra months to the calendar to reconcile the two types of years.
Zev Steinhardt
As others have pointed out, the Hebrew calendar has a different number of days in the year than the Gregorian. In order to keep them in sync, a month of 30 days is added seven out of every 19 years (in years 3,6,8,11,14,17 & 19) right before Passover.
Zev Steinhardt
Neat. Thanks.
For anyone out there that knows, I assume the Chinese lunar calendar works in a similar fashion, yes?
–Cliffy
BTW, the lunar calendar is short by 11.something days per solar year. The “leap month” system of calendar adjustment is known as the Metonic Correction, after the fella (Meton, a Greek astronomer) who thunk it up.
I have to say, a lunar calander is awkward, but it has one big advantage: you can tell the phase of the moon just by looking at the calender.
Not that anyone asked, but the word draydel is a Yiddish word derived from the German drehen, which means “to turn.” The Hebrew name for draydel is * sevivone*, from the root * savov*, meaning “to turn.”
Draydels used before the State of Israel had the following Hebrew letters on them: nun, gimmel, hay, shin. These letters stood for the Hebrew words nes gadol haya sham, meaning “a great miracle happened there.” After the State of Israel was created, shin was changed to pay for po, meaning “here.”
Of course, even in the solar calendar systems, you can tell the phase of the moon just by looking at the, um, moon. 
–Cliffy
So, to answer the initial question, Chanukah starts on the 25th day after the new moon.
The question of “which new moon?” involves the complexity of the Hebrew lunar calendar, as aforementioned.
And knowing the phase of the moon is valueable, because …?
Well, if you’re a werewolf, you’ll want to know when to chain yourself up…
Either that, or they stand for the Yiddish words “nisht”, “gantz”, “halb”. and “shtel” (nothing, everything, half, put in), until people took an old gambling game and said, “Hey, lets make it symbolic!”
I think it’s because the Jewish calendar, like other early calendars, was developed long before people understood the astronomy of the solar system – that the earth revolves around the sun, and a year (in the sense of a cycle of seasons) corresponds to one revolution of the earth around the sun.
If you don’t know much about astronomy, basing a calendar on the phases of the moon seems understandable, since it’s the most obvious “cycle” that you can observe in the heavens.