For purposes of discussion, the answer to the question – “what is the relationship between Mordred and King Arthur?” – drew upon Sir Thomas Malory’s Le Morte D’Arthur, a link to the complete text to which is provided below. While Sir Malory is not believed to have originated the legend of King Arthur and the knights of the Round Table, his version of the story remains the most respected in all of literature. Written while Sir Malory languished in prison, where he would die in 1471, Le Morte D’Arthur would not be published for another 14 years, when William Caxton, an English writer and the first to use a printing press in England, printed a copy of Sir Malory’s work.
There are a number of references to Mordred in Le Morte D’Arthur that suggest the nature of his relationship to King Arthur. What makes those passages particularly ironic is that they describe a conception not unlike that which brought Arthur himself into the world. In Book I, Chapter II, Malory describes an affair between the reigning king of England and the wife of the Duke of Cornwall, the beautiful Ingraine:
“King Uther lay with Igraine more than three hours after his death, and begat on her that night Arthur . . .”
After Arthur’s own rise to the throne, his own illegitimate beginning replays itself when he sleeps with the wife of a fellow monarch, King Lot. As Malory describes the situation in Book I, Chapter XIX:
“For she was a passing fair lady, therefore the king cast great love unto her, and desired to lie by her; so they were agreed, and he begat upon her Mordred, and she was his sister, on his mother's side, Igraine.” (Igraine being Arthur’s mother)
To clarify, then, King Arthur sleeps with his fellow king’s wife, Morgause, who, unbeknownst to Arthur, is actually his sister. The result of that affair is the birth of Mordred. Mordred’s origins are again described in Book II, Chapter X:
“. . .and for King Arthur lay by King Lot's wife, the which was Arthur's sister, and gat on her Mordred, . .”
That Mordred, Arthur’s bastard son, should play a major role in the king’s ultimate demise is prophesied by Arthur’s counsel, the wizard Merlin, who notes in Book II, Chapter XI:
“After this Merlin told unto King Arthur of the prophecy that there should be a great battle beside Salisbury, and Mordred his own son should be against him.”
So, in conclusion, Mordred is King Arthur’s illegitimate son and eventual mortal enemy.