It is not a regular Notary Public stamp but a form of authentication issued to documents for use in foreigners countries: requested only to US Citizens.
With this certification by the Hague Convention apostille, the document is entitled to recognition in the country of intended use, and no certification by the Authentications Office or legalization by the embassy or consulate of the foreign country where the document is to be used is required. The Authentications Office only certify to documents from other federal agencies and officials from foreign governments with the apostille.
The Department of State, Authentications Office is responsible for signing and issuing certificates under the Seal of the U.S. Department providing authentication services to U.S. citizens and foreign nationals on documents that will be used overseas.
The apostille is a document stapled to your original document by the Secretary of State Notary Public and has to be placed on birth/divorce/death certificates, required for your Civil Wedding in Italy.
If you are a Naturalized US Citizen: your naturalization certificate will substitute for your birth certificate and must be apostilled.