Formerly, when someone wanted a public document such as a court judgment or acknowledgment by a notary recognized in another country, it was necessary to go through a cumbersome process of authentication known as "legalisation", which was often bureaucratic, slow and expensive.  The Hague Convention of 5 October 1961 Abolishing the Requirement of Legalisation for Foreign Public Documents reduces the authentication process to a single formality: the issuance of an authentication certificate, known as an apostille, by an authority designated by the country where the public document was issued.  Under this treaty, each country designates a competent authority that are authorized to issue apostilles.  The list of U.S. authorities is available here. 

The California Secretary of State is on the U.S. list of competent authorities and the Secretary of State's website provides detailed information on how to request an apostille here.   Only one California statute, Civil Code Section 1183, mentions apostilles.  That statute concerns the proof or acknowledgment of instruments outside the United States.