Belgium was a country on Earth, part of the European Alliance. Cities included Brussels, Antwerp and Waterloo. This region, like Armenia, was identified by Captain James T. Kirk in 2267 as a vulnerable waypoint situated on the invasion routes of many invading armies in Earth's history. The flag of Belgium was three vertical bands of black, yellow, and red. (TOS: "Errand of Mercy"; ENT: "First Flight")
In the alternate timeline 20th century created by Vosk and the Na'kuhl, Vladimir Lenin was assassinated, and Adolf Hitler could focus on the West. He took France, then Belgium and the Netherlands quickly fell. (ENT: "Storm Front, Part II")
In the late 20th century, Belgium was a founding member of the European Space Agency. (ENT: "First Flight")
In 2325, Devinoni Ral was born here. (TNG: "The Price")
In 2372, Antwerp was targeted by the Dominion. A changeling infiltrator detonated an explosive device there. (DS9: "Homefront")