On a literal level, when Arthur leaves the court to fight Lancelot over his presumed affair with Guenivere, he places Mordred on the British throne. Mordred begins to form allegiances with false promises, and the people resist Arthur's return. At this level, the war is a power grab, and Arthur fights the civil war to regain his throne.
On a more symbolic level, we sense that Mordred stands for an inner force, caused by human failing (Arthur's affair with Morgause). Camelot was superior to all other nations and could not be defeated in battle. Its weakness is internal, like a classical "hamartia" (fatal flaw). Mordred represents the consequence of Arthur's and Camelot's weakness.
Without Launcelot or Gawain, Arthur returns to claim his throne profoundly lacking in his most trusted companions. He was warned to not fight until Launcelot could rejoin Arthur, but in the fatal truce ceremony, a snake accidentally crosses a knight's foot. Instinctively, he draws his sword to kill the snake, but this is misread as a sign of aggression and a betrayal of the peace terms. War breaks out at this point.
This seemingly meaningless accident leads to the brutal battle that leaves only a handful of Camelot's knights standing. In this way, we can read the war as a series of accidents and betrayals dating back to Arthur's affair, Launcelot and Guenivere's affair, Gawain's wounds from fighting Launcelot, Launcelot's delay in coming to Arthur's aid, Mordred's political contrivances rather than honor, and a snake.