Nothing. December 25 is an ordinary weekday in Judaism. The Jewish religious festival of Hanukkah is celebrated in December or late November. It has no connection to any Christian occasion. Hanukkah was instituted 2180 years ago.
For more about Hanukkah:
Jesus and some people we might know.
Almost all Jews celebrate Hanukkah.
They don't. Jews believe that Jews should celebrate Hanukkah.
All Orthadox Jews Celebrate Chanukkah, almost all non-Orthodox Jews also celebrate it as well.
Jews in California celebrate Yom Kippur the same way that Jews the world over celebrate Yom Kippur.
They celebrate Shabbat and Havdalah.
Irish Jews celebrate Passover the same way as Jews all over the world.
There are always Jews who celebrate Passover regardless of the location or circumstances. Jews celebrated Passover in the ghettos, and then in the concentration camps.
Orthodox Jews often do not celebrate Thanksgiving because they see it as a sign of assimilation. Liberal and Secular Jews do not have this issue and usually do celebrate Thanksgiving (if they are American).
Only the Jews in Mexico celebrate Hanukkah.
Jews.
we don't.