Duncan is the king on whose behalf Macbeth and Banquo fight against the rebel Macdonwald and Sweno (King of Norway) and his ally, the treacherous Thane of Cawdor. It seems that Shakespeare may be assuming the Scottish method of deciding a king's heir--often by vote of the thanes, especially if the king's son is young. When Duncan tries to secure the succession to his son Malcolm as Prince of Cumberland (in 1.4), this causes Macbeth (who has just saved Duncan's crown) to resolve on action, despite his earlier decision to let fate "crown" him if the prediction is correct. See Background: Sources for further information about the historical figure of Duncan.