1) Some have the custom to eat dairy foods on Chanukah because one of the miracles of Chanukah came about through them — Yehudis, daughter of Yochanan the Kohen Gadol, fed cheese to the leader of the enemy so he would become thirsty and then she gave him much wine. After he became intoxicated, she killed him. (Shulchan Aruch and Mishnah Berura, section 670)
2) The Shabbos meal of Chanukah should be larger than those of the rest of the year. Similarly, the meal on Rosh Chodesh Teves should be enhanced in honor of Chanukah. (ibid.)