There are many "traditional" dinners made by families throughout Italy on Christmas Eve, but most involve some sort of fish as it is usually observed as a day of fasting from meat. A popular tradition known in the south of Italy is the "Feast of the Seven Fishes" which, as the name implies, is loaded with local fish baked or fried.
But in families throughout Italy, it would be common to serve Baccala, a salted cod that has been soaked in water for 2 to 3 days. Because of its preservation, salted cod was a popular holiday choice especially for people living away from the coast.
It is very versatile and can be fried or baked. A very simple way to prepare it is to coat it in flour and then fry it in olive oil. (make sure you soak it and change the water several times) A nice condiment is friggione, or onions braised for hours in tomatoes. Friggione is typical Bolognese. You can also serve it over grilled polenta.