Apostille certification is a fancy name for a bureaucratic procedure by which official documents issued in one country are certified in a uniform way, so that they become formally acceptable in another country. This procedure was established in 1961 under the Hague Convention, and nowadays almost all countries of the world are part of this Convention.
In the Apostille process, the signature of the officer, who has certified the document locally (usually, the Notary) is authenticated by a second-tier certification. A special stamp or sticker, called Apostille, is attached to the document, on top of the Notarial inscription. Contrary to a popular view, the Apostille does not confirm the contents of the document. It merely certifies that the first-tier certifier – the Notary – has been real, and had the appropriate rights and powers to make the underlying certification in the first instance.
Apostille is usually issued by a designated government office, like the Foreign Office or the Supreme Court of the country.