Hanukkah ~

Hanukkah is not a “substitute Christmas.” It is a valid, albeit minor, Jewish holiday that commemorates the victory that the Maccabees had over the tyrannical Antiochus Epiphanes, and the subsequent cleansing and rededication of the Temple. The account is found in the apocryphal writings, Maccabees. Although it is not one of the feasts directly commanded by God, it was observed even before the time of Christ, and is mentioned in John 10:22 and 23.
Hanukkah is also known as the Festival of Lights. The reason why lights play such an important role in the holiday observance is that they commemorate the legendary miraculous provision of holy oil with which the lampstand was rekindled at the rededication of the Altar.
As to the giving of gifts, this means of expressing joy finds its precedent in the Book of Esther, the Scriptural basis for another of the minor Jewish holidays, Purim. There the Jews sent gifts to one another as they rejoiced at the defeat of Haman’s plot to destroy them. Despite this precedent, however, it’s a safe guess that the idea of gift giving gained momentum within the Jewish community in direct reaction to the commercialization of Christmas by the Gentile community. You see, it’s easier for Jewish parents to tell their children, “We Jews don’t celebrate Christmas” when there is a pleasant alternative, replete with just as much merriment, gifts, and decorations.
In answer to the question about Jewish believers celebrating Hanukkah — yes, many do. There is no contradiction between the two holidays, as they commemorate two entirely different events, both worthy of celebration. In fact, there are some interesting parallels to these two holidays ~