A kingdom is a state ruled by a monarch, sometimes called a monarchy. Power is usually passed along hereditary lines. In Azeroth, this is the most common form of government for human states. Most likely the predominance of this type of state on the eastern continent explains why it is called the Eastern Kingdoms.
The two great remaining kingdoms of Azeroth are Kingdom of Ironforge and Stormwind. Other surviving human kingdoms include Gilneas and Kul Tiras, while Lordaeron, Stromgarde and Alterac have been destroyed as political entities.
The high elves of Quel'Thalas were ruled by a king (the Sunstrider dynasty, with some power being held by the Council of Silvermoon.
Other types of government
The shielded city-state of Dalaran is ruled by a group of mages called the Kirin Tor, under a system referred to as a magocracy. The orcs, trolls, tauren, and various other races are ruled by a clan-based or tribal system, while the night elves share power between the leaders of their two main religious groups, the followers of Elune and the druids. The gnomish survivors of Gnomeregan are led by an elected official called the High Tinker.