The Authority is the organization responsible for the assignment of domain names and the management of the registry and the primary nameserver for his TLD. Every "geographic" TLD is assigned to an Authority. For the .IT domains (Italy) the responsible for the assignment is at the Institute for Telematic Applications of CNR in PISA. Into this institute works the Naming Authority and the Registration Authority.
Some "international" domains (.COM, .NET, .ORG) are managed by an independent organism that promotes the development of these TLDs all over the world. These extensions were born in the USA but they don't have a specific location, so they can be registered by anybody and they are not subjected to the strict rules of the Authorities of other countries.