The United Nations (UN) is a intergovernmental organization tasked to maintain peace and international order around the world and to promote international cooperation. The UN founded a department for military operations similar to its peacekeeping program called the United Nations Interplanetary Corps with the purpose of providing protection for Earth and the Solar System. The headquarters of the UN is situated in Manhattan, New York City.
The UN was established after World War II as an international organization facilitating cooperation in, among other areas, international law. It was a replacement for the inefficient League of Nations around 1945. The United Nations suceeded the League of Nations, a similair international organization formed in 1919 to work for peace following the First World War.
Based on observation of the events in Aliens: Steel Egg, the United Nations became strengthened beyond its original intent over the decades, as the UNIC controlled most of the territories in the Solar System (including Earth). So it may be possible that the strengthened form of the UN was the government of Earth at the time of Aliens: Steel Egg.