King is the title given to a male monarch in a variety of contexts. The female equivalent is queen regnant (while the title of queen on its own usually refers to the consort of a king).
In the context of prehistory, antiquity and contemporary indigenous peoples, the title may refer to tribal kingship. Germanic kingship is cognate with Indo-European traditions of tribal rulership (c.f. Indic rājan, Gothic reiks, and Old Irish rí, etc.)
In the context of classical antiquity, king may translate Latin rex or either Greek archon or basileus.
In classical European feudalism, the title of king as the ruler of a kingdom is understood as the highest rank in the feudal order, potentially subject, at least nominally, only to an emperor (harking back to the client kings of the Roman Empire).
In a modern context, the title may refer to the ruler of one of several modern monarchies (either absolute or constitutional). The title of king is used alongside other titles for monarchs, in the West prince, emperor, archduke, duke or grand duke, in the Middle East sultan or emir; etc.
The English term king is derived from the Anglo-Saxon cyning, which in turn is derived from the Common Germanic *kuningaz. The Common Germanic term was borrowed into Estonian and Finnish at an early time, surviving in these languages as kuningas. The English term "king" translates, and is considered equivalent to, Latin rēx and its equivalents in the various European languages. The Germanic term is notably different from the word for "king" in other Indo-European languages (*rēks "ruler"; Latin rēx, Sanskrit rājan and Irish ríg, but see Gothic reiks and, e.g., modern German Reich and modern Dutch rijk). It is a derivation from the term *kunjom "kin" (Old English cynn) by the -inga- suffix. The literal meaning is that of a "scion of the [noble] kin", or perhaps "son or descendant of one of noble birth" (OED).
English queen translates Latin regina; it is from Old English cwen "queen, noble woman, wife" from the PIE word for "woman" (*gwen-). The Germanic term for "wife" appears to have been specialized to "wife of a king"; in Old Norse, the cognate kvan still mostly refers to a wife generally. Scandinavian drottning, dronning is a feminine derivation from *druhtinaz "lord".
The English word is of Germanic origin, and historically refers to Germanic kingship, in the pre-Christian period a type of tribal kingship. The monarchies of Europe in the Christian Middle Ages derived their claim from Christianisation and the divine right of kings, partly influenced by the notion of sacral kingship inherited from Germanic antiquity.
The Early Middle Ages begin with a fragmentation of the former Western Roman Empire into "barbarian kingdoms". In Western Europe, the kingdom of the Franks developed into the Carolingian Empire by the 8th century, and the kingdoms of Anglo-Saxon England were unified into the kingdom of England by the 10th century.
With the breakup of the Carolingian Empire in the 9th century, the system of feudalism places kings at the head of a pyramid of relationships between liege lords and vassals, dependent on the regional rule of barons, and the intermediate positions of counts (or earls) and dukes. The core of European feudal manorialism in the High Middle Ages were the territories of the kingdom of France, the Holy Roman Empire (centered on the nominal kingdoms of Germany and Italy) and the kingdoms of England and Scotland.
During the European Middle Ages, the European kingdoms underwent a general trend of centralisation of power, so that by the Late Middle Ages there were a number of large and powerful kingdoms in Europe, which would develop into the great powers of Europe in the Early Modern period.
In the Iberian Peninsula, the remnants of the Visigothic Kingdom, the petty kingdoms of Asturias and Pamplona, expanded into the kingdom of Portugal, the Crown of Castile and the Crown of Aragon with the ongoing Reconquista.
In southern Europe, the kingdom of Sicily was established following the Norman conquest of southern Italy. The Kingdom of Sardinia was claimed as a separate title held by the Crown of Aragon in 1324. In the Balkans, the Kingdom of Serbia was established in 1217.
In eastern-central Europe, the Kingdom of Hungary was established in AD 1000 following the Christianisation of the Magyars. The kingdoms of Poland and Bohemia were established within the Holy Roman Empire in 1025 and 1198, respectively. In Eastern Europe, the Kievan Rus' consolidated into the Grand Duchy of Moscow, which did not technically claim the status of kingdom until the early modern Tsardom of Russia.
In northern Europe, the tribal kingdoms of the Viking Age by the 11th century expanded into the North Sea Empire under Cnut the Great, king of Denmark, England and Norway. The Christianization of Scandinavia resulted in "consolidated" kingdoms of Sweden and Norway, and by the end of the medieval period the pan-Scandinavian Kalmar Union.