Well, we eat, and we argue about politics, which is what we do most days of the year….
Italy being a Catholic country, on Christmas Eve is de rigeur to eat fish: I believe its origin resides in the necessity to fast before an important religious event. Abstaining from meat is a softer version of fasting, and fish is a good alternative.
Nowadays the real fasting requirement has been completely forgotten, as il Cenone della Vigilia (‘the big dinner of the Eve’) competes in size with the main Christmas and New Year’s meals. Italy having so much coastline, every region has its own version of the traditional dinner with local specialties: where I come from, Bologna, we usually have eel (grilled or stewed) which is typical of the Ravenna region nearby. Typical is also baccalà, dried and salted cod, which is cooked in as many ways as there are Italian villages.
On Christmas day, it is a meat feast: many regions have their own type of stuffed pasta. In Bologna you have tortellini (in broth or with cream) or lasagne, followed usually by a roast, which can be chicken, beef or pork, or often also guinea-fowl. It is not traditional to eat turkey in any region, as far as I’m aware. You also may have lesso, a cut of meat which has been used to make broth (for the above tortellini), which is then eaten with sauce (a green sauce made with capers, parsley and anchovies).
For dessert it is obligatory to consume a slice of panettone or pandoro (the former with candied peel and raisins, the latter a simpler sponge), which are original or Milan and Verona respectively but have spread throughout the peninsula. The tastier (but less traditional) ones are filled with chocolate or liqueur creams.
Another typical sweet is torrone, made of egg white, honey (or sugar) and almonds – it used to be rock hard but most of them nowadays are a bit softer (and a lot nicer to eat!).