It's the receipt the post office gives you when you submit a kit postale for a residence permit. It proves the application was filed on a given date and is needed for many follow-up steps.
While you wait for the actual card, the ricevuta acts as proof that you have an active application. Combined with a valid expired permit, it usually keeps you legal during the renewal.
"While his new permit was being processed in Foggia, Adnan used his ricevuta to renew his work contract, open a new bank account, and request a CIE update."
Travel rules with only a ricevuta are tricky. Travelling outside Italy on a receipt during a first application is usually not allowed. For renewals, rules are more flexible but still limited.
Official source
Polizia di Stato
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