Arthur also has a half-sister (she has different roles and different versions), Morgan Le Fay. She believed that she was the rightful heir to the thrown because she was the first child of King Uther. She made multiply attempts to take the thrown, one being that she slept with Arthur and conceived a son, Mordred. The boy was raised to hate Arthur which fueled his position in Arthur's downfall. Morded was able to help with the plan to bring down Arthur because he was one of the knights of the round table.
Role in the Story
He's the main character and the hero of the story and without him there wouldn't have been the legend of King Arthur.
All this lead to the fall of Camelot. War begins and Arthur dies in battle (in most versions they all end with Arthur dying in some form of battle or war). Although many versions have him dying in different battles against Saxons, Lancelot, Mordred, Morgan Le Fay, Romans, etc.