the 25th day of Kislev and the 2nd day of Tevet on the Hebrew calendar coincide.
There is no relation between Christmas and Hanukah.
About t 200 years ago, the Greek ruler Antiochus and his people tried to impose their religious practices upon the world. The Jews would not accept that and the Maccabees, a group of Jewish fighters, overcame the armies of Antiochus.
When they returned triumphantly to Jerusalem, they discovered that their enemies had desecrated the Holy Temple. They cleaned up the mess and found only one jar of sacred oil. This one jar was only enough to keep the Holy Light burning for one day. The Jews decided to use the one jar, and went away to obtain additional oil.
This journey took 8 days, and when they returned, they discovered that the Holy Light was still burning from the one jar of oil. This was proclaimed a miracle.
When Hanukah is celebrated, nine unlit candles are placed in a candelabrum that is called a Menorah. The eight candles represent the eight days and nights of the Miracle of the oil. The ninth candle is used to light the other eight candles.
On the first night of Hanukah one candle is lit, and each night an additional candle is lit from right to left, until on the eighth night all nine candles burn. Before each candle is lit, prayers and blessings are said.