What is the AIRE?

In this episode, Italian attorney Marco Permunian and co-host Rafael Di Furia talk about the AIRE (L'Anagrafe degli Italiani Residenti all'Estero/Registry of Italian Citizens Residing Abroad). What is it? How do you register with the AIRE? What is the AIRE for? Do you have to register with the AIRE? What are the benefits of the AIRE?