One of the many varied spellings of the Jewish equivalent of Christmas, connotation-wise anyway. Other popular spellings include chanukah, hanukah, and chanukkah. (Hebrew, being a phonetic language with no clear mapping with Roman characters, often leaves plenty to preference in transliteration.)

The official reason for this particular Winter celebration is completely different than Christmas. Whereas Christmas is, among a very modernized and high-bullshit attempt to get rid of various Pagan festivities, namely Saturnalia, a celebration of the birth of Jesus Christ (regardless of when it actually happened, and it certainly wasn't on Saturnalia), Hanukah celebrates a mytho-historical battle in which the pacifist Hebrews, captured by the persecuters (as are all-too-common in Jewish mytho-history, as well as the Real World), were trying to defend themselves, and ran short on lamp oil. Somehow a single day's supply lasted for eight; the dreidel, a toy played with on Hanukah (though I haven't touched one in years), was a trick the Hebrews who were captured used to discuss plans with guards watching under the guise of the game, has thus become a game kids actually play (for chocolate coins) where it has been inscribed with a Hebrew acronym for "A great miracle happened here." The miracle being the whole eight-day oil thing. Lots of candles and presents, too.

I think the only reason Jews almost always celebrate Hanukah and not as often the other similar holidays (such as Purim, which is basically the same story as the Hanukah story except that the Jews actually fought back and there wasn't any supposed miracle) is because it happens to coincide with Christmas, and gives Jewish kids their own chance to cash in on over-commercialized Saturnalia fun under a typical Judeo-Christian guise of celebration of some pivotal miracle.