What day in December is Hanukkah celebrated?

The Jewish calendar is a lunar calendar, whilst the Gregorian calendar is a Solar Calendar, therefore they have different months.

Often the Hebrew month of Kislev, which is the month in which Chanuka falls, will correlate to the Gregorian month of December, so it is common for Chanuka to fall in December.

The way the Hebrew calendar is formed, the correlation between with the Gregorian months do not vary a great deal, as leap years occur periodically keeping the Hebrew months in the same season each year. This differes from the Islamic calendar, which is a purely lunar calendar - explaining why the month of Ramadan will occur at a different time of the Gregorian calendar every year.