The Hague Convention that is referenced to the Apostille Process is the 1961 Hague Convention Abolishing the Requirement of Legalization for Foreign Public Documents of the Hague Conference on Private International Law. This particular convention basically outlined the necessary process and certifications required for a document generated and Authenticated in one member country (sometimes referred to as states) to be accepted by another member country (state) without further process.
This process is usually referred to as Legalization. The Apostille (sometimes referred to as Authentication) simplifies and speeds up the process for the acceptance of a qualifying document from one member country (state) to another.
To reiterate, the Hague Convention of 1961 Abolishing the Requirement of Legalization of Foreign Public Documents is an international agreement which simplified the Authentication process of public documents to be used in nations that are members of the 1961 Hague Convention. The United States signed this agreement on October 15, 1981. Only those nations who are party to the Hague Apostille Convention recognize Apostille Certifications.
Listed below are the current countries, members of the Hague Apostille Convention. All non-federal documents destined for these countries only require an Apostille from the Secretary of the State.