A cornicello, corno, or corno portafortuna is an Italian amulet or talisman worn to protect against the evil eye (il malocchio) and bad luck in general, and, historically, to promote fertility and virility. In the Neapolitan dialect, it is called curniciello or variants thereof.
The origins of this talisman can be traced back to neolithic times (really!) where it was a custom to hang the horns of animals one had slaughtered at the entrance of the cave, as a symbol of power and to protect the home.
In Greek mythology, Zeus broke a horn off a goat, filled it with fruit and flowers and gave it to his caretaker - this cornucopia or horn of plenty came to represent prosperity and abundance.
The coral of which the talismans are often made is sacred to Venus, goddess of love, fertility, sex, and prosperity.
Silver, of which it is also often made, is sacred to Luna, goddess of the moon, and is also a powerful protective metal.
The phallic shape is also a reference to Priapus, a Greek male fertility god; phallic shapes were long considered powerful fertility symbols for the ancient Greek and Roman people and evidence of this can be seen in the surviving frescoes and stone carvings of the phallus at Pompei.
The traditional cornicello is red which represents vitality and strength, since the colour brings to mind blood and fire.
If you visit the city of Naples (Napoli) on the coast of the Campania region, you'll see cornicelli for sale in the many tourist shops, in street markets/stalls, printed on t-shirts, in jewellers'... basically everywhere. It's one of the symbols of the city most recognised world wide.
One of the "traditions"of the cornicello is that it should always be given as a gift for maximum protective power, and when giving the gift the gift-giver should press the point of the talisman into the palm of the receiver's left hand...