It's a power of attorney: a formal document that lets someone else do legally binding things in your name, like buying a house, opening a bank account, or accepting an inheritance. In Italy you sign it in front of a notaio; if you're abroad, the Italian consulate can play the notary's role. It can be general (procura generale) or limited to one specific act (procura speciale).
It's how things get done in Italy without you being there. Expats use it to let a lawyer or relative close a property purchase, manage an inheritance, or push paperwork forward while they're still in their home country waiting for a visa.
"Still waiting for her visa in Casablanca, Imane signed a procura speciale at the Italian consulate. With it, her lawyer in Alessandria signed the deed for her new apartment without her setting foot in Italy."
Don't mix it up with a delega, the informal signed letter used for small errands. A procura is notarised and covers legally binding acts. Also, "la Procura" with a capital P often means the public prosecutor's office (Procura della Repubblica). Context tells you which one is meant.
Official source
Ministero degli Affari Esteri (atti notarili)
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