According to Geoffrey of Monmouth's Historia Regum Britanniae, Uther falls in love with Igraine and wars with Gorlois to get to her. Uther asks for Merlin's aid in pursuing her, and Merlin casts a spell that disguises Uther in the form of Gorlois. As Gorlois, he approaches his love easily and they sleep together, conceiving Arthur. Unbeknownst to either of them, the real Gorlois has been killed in his castle that very night. Eventually Igraine is convinced to marry Uther.
Later treatments such as the Vulgate Cycle and Sir Thomas Malory's Le Morte d'Arthur expand on this outline by having Gorlois' daughters married off to Uther's vassals; Elaine to King Nentres, Morgause to King Lot, and after receiving an education in a convent, Morgan to King Urien. Arthur is spared any knowledge of this when he is whisked away by Merlin to be raised by Sir Ector.