An apostille is essentially a certificate of authenticity. Since October 15, 1981, the United States has been part of the 1961 Hague Convention abolishing the Requirement of Legalization for Foreign Public Documents. The convention provides for the simplified certification of public (including notarized) documents to be used in countries that have joined the convention. Under the Hague Convention, signatory countries have agreed to recognize public documents issued by other signatory countries if those public documents are authenticated by the attachment of an internationally recognized form of authentication known as an "apostille."
NOTE: If you're using the diploma or transcript in a country not listed in the signatory countries, you will need to contact the embassy or consulate of the country where you intend to use the document to discuss their authentication requirements. (Some non-signatory countries may accept an apostille. Others may require further steps such as U.S. Department of State certification then consular certification).