It's a simple signed letter authorising someone to run an everyday errand for you: collect a parcel or certificate, hand in documents at the comune, or attend a condominium meeting. No notary involved: you write it, sign it, and attach a photocopy of your ID. Many offices have their own one-page delega form to fill in.
It saves you a day off work every time an office wants something "in person" that doesn't legally require you personally. Most counters accept a delega plus two ID copies (yours and the delegate's), so a friend can queue for you.
"Farid couldn't leave work to collect his language-course certificate in Novara, so he wrote a delega for his flatmate, who picked it up with the letter and photocopies of both their ID cards."
A delega won't work for everything. Some steps require you personally, like giving fingerprints for a permesso di soggiorno, and legally binding acts need a notarised procura instead. When in doubt, ask the office whether they accept a delega semplice before sending someone.
Official source
DPR 445/2000, art. 38 (Normattiva)
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