King Arthur is said to be the son of Uther Pendragon and Igraine of Cornwall. He is a mythic figure in Celtic stories like Culhwch and Olwen. Early Latin chronicles show him as a military leader. And in later romantic literature he is shown as a king and emperor.
The debate on whether he was a real or solely a literary figure has been debated since Renaissance. At that time the Tudor kings of Britain portended to trace their lineage to King Arthur as a justification for their position on the English throne. Modern scholars have generally believed that there was an actual person as the inspiration for the legends, but not a king with a group of knights in shining armour.
If there is a historical basis for King Arthur, he would have to have existed in the late 5th or early 6th century, after the Romans had left Britain, and before any English literature existed. King Arthur would have had to be a warrior king fighting the waves of Northern European invaders that flooded into the vacuum that was left after the Romans left Britain. Any earlier and he would have been recored in Roman history, much later and he would have been recorded by later English historians.
The rub is that there is no conclusive evidence for or against King Arthur in history. He could have existed, but absense is not proof in itself that he did exist.
Later writers wove the early mentions of King Arthur into the full blown legend as penned by Malory to Tennyson to T. H. White. The central pillar of myth is the downfall of Arthur's kingdom brought about by the treachery of Mordred and which is made possible because of the love of Lancelot for Arthur's wife, Guinevere.
Arthur, who was he?