Morgause does not appear in the historical texts. Geoffrey of Monmouth says Lot was married to Anna, Arthur's half-sister, not Morgause. But Malory introduces the Morgause as being wife of Lot, King of Orkney. Morgause has a minor, but important role in Arthurian legand, and is frequently blurred with her more infamous sister, Morgan le Fay.
According to Thomas Malory, Morgause is one of the three daughters of Igrayne and the Duke of Cornwall, so a half-sister to Arthur. As the wife of King Lot she became the mother of Gawaine, Gaheris, Agravaine, Gareth, and Mordred.
Morgause commits incest when she sleeps with Arthur and conceives Mordred. In the French Vulgate cycle Arthur is attracted to King Lot's wife and deceives her into thinking he is her husband. It is only later that Arthur realizes he has committed incest. Mordred is the son produced from their tryst.
Thomas Malory's Le Morte d'Arthur says that Morgause did not know of her blood relationship to King Arthur when Mordred was conceived. She is portrayed by Malory as a generally "good" character" whose only real sin is her adultery. Arthur's seduction of his wife, causes Lot to for a lifelong hatred of Authur. And it is the adultery of Morgause that brings about her death - Sir Gaheris, her son, finds his enemy Sir Lamerak in bed with his mother, Morgause. And in a fit of rage, kills his mother.
In modern adaptations of the Arthurian legend the incest is largely engineered by Morgause herself, and she using their son Mordred as a tool to destroy his father.