It's the application form for requesting a codice fiscale at the Agenzia delle Entrate. The shorter Modello AA4/8 is for individuals. You fill it in, attach a copy of your ID, and hand it over at the counter.
Without filling in this form (or its consular equivalent), you don't get a codice fiscale, and without that you can't do almost anything official in Italy.
"On his second day in Voghera, Jurgis filled in a Modello AA4/8 at the Agenzia delle Entrate, handed it in with his passport, and walked out with his codice fiscale on a paper slip."
Many people apply through their employer or landlord, who provides the form. The form is the same. The procedure just goes through someone else representing you.
Official source
Agenzia delle Entrate
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