Serbia and Montenegro was a country in the Balkans, created from the two remaining republics of Yugoslavia. The republics of Serbia and Montenegro together established a federation in 1992 as the Federal Republic of Yugoslavia (FRY). In 2003, it was reconstituted as a state union officially known as the State Union of Serbia and Montenegro.
The state union effectively came to an end after Montenegro's formal declaration of independence on 3 June 2006, and Serbia's formal declaration of independence on 5 June. After the dissolution, Serbia continued to be the legal successor of the union, while Montenegro re-applied for membership in international organizations.
A full history can be found on the Wikipedia page