Registered Residence (Anagrafe)
Plain English
Your officially registered home address with your local comune, recorded in the anagrafe (the civil registry). It says you actually live at that address habitually, not just that you receive mail there.
Why it matters
You need it for an Italian ID card, the SSN GP enrolment, the prima casa tax break, voting in local elections (for EU citizens), and pretty much any tax-related benefit. After you sign a long lease, you have to request it.
Real example
"Once Pedro signed his rental contract in Cagliari, he went to the comune to request residenza. A few weeks later a vigile rang the bell to check he really lived there. The certificate came in the mail soon after."
Common confusion
Residenza is different from domicilio. Residenza is where you actually live and is registered. Domicilio is where you receive mail or do business, and doesn\'t need to match.
Official source
Ministero dell'Interno (Anagrafe Nazionale)