It's the certificate EU citizens get from the comune once they've been registered as residents in Italy. It replaces the residence permit for EU nationals, who don't need a permesso to live here.
It proves you're legally living in Italy. Banks, employers, and landlords often ask for it. After 5 years of continuous residence, EU citizens can request the permanent version.
"After moving from Berlin to Como for work, Lukas registered at the comune within 90 days. A few weeks later he picked up his attestato di iscrizione anagrafica, which his bank had been asking for."
It's only for EU citizens (and EEA + Switzerland). Non-EU citizens go through the permesso di soggiorno process instead.
Official source
Ministero dell'Interno
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