APOSTILLE is a form of authentication issued to documents for use in countries that participate in the Hague Convention of 1961. Here in the U.S., it is provided by the Office of the Secretary of State of the State where the document/certificate was issued.
NOTE: The Apostille is not a stamp on the certificate. It is a legalization, i.e. a document stapled to the birth/marriage/death certificate by the Secretary of State
If you are applying for Italian Dual Citizenship, U.S. Birth/Marriage/Death records related to the "Italian side" must bear an APOSTILLE (according to Hague Convention of Dec. 5, 1961) of the Secretary of State of the State in which the document was issued, (except for the Certificate of Naturalization and/or similar documentation).