The "codice fiscale" (fiscal code) is an identification number needed to sign up for italian public health insurance (for non-EU citizens), to open a bank account, to draw up a rental agreement or to purchase a SIM card.
It is issued by the Agenzia delle Entrate, by presenting a valid Identity Document or a passport.

Web sites:
-> Local office of Agenzia delle Entrate
-> Information on Codice Fiscale
-> Forms