Duncan is the King of Scotland. While spending the night as a guest at Inverness, he's murdered by Macbeth, who has aspirations to rule the country. In the play, Duncan is a benevolent old man. We never see him out on the battlefield, and he is always full of kindly words. He's also generous when bestowing honors on the soldiers and thanes that protect him and his kingdom. Duncan is so sympathetic and likable a character that murdering him seems horrifying. His good nature, pronounced by Macbeth in his private thoughts, reminds us of what a terrible thing it is to murder him. Even Lady Macbeth, who says she would murder her own nursing babe, can't kill him because he resembles her father while sleeping. That Macbeth can murder this man exemplifies just how atrocious the act is. It's also a clear indication that Macbeth is far removed from human kindness and morality.
King Duncan's character is also interesting insofar as it speaks to the play's representation of masculinity and power. Shakespeare scholar and retired UC Berkeley professor Janet Adelman reminds us that in a world where manhood is synonymous with violence and cruelty, King Duncan is decidedly soft: "Heavily idealized, this ideally protective father is nonetheless largely ineffectual: even when he is alive, he is unable to hold his kingdom together, reliant on a series of bloody men to suppress an increasingly successful series of rebellions…For Duncan's androgyny is the object of enormous ambivalence: idealized for his nurturing paternity, he is nonetheless killed for his womanish softness, his childish trust, his inability to read men's minds in their faces, his reliance on the fighting of sons who can rebel against him" (Suffocating Mothers: Fantasies of Maternal origin in Shakespeare's Play, Hamlet to The Tempest).
In this way, King Duncan is a lot like the historical figure Duncane from Shakespeare's main source for the play, Volume II of Holinshed's Chronicles of England, Scotland, and Ireland. In Chronicles, Duncane is too "soft and gentle of nature" and is contrasted with Macbeth, who is "cruel of nature." Shakespeare picks up on this contrast in Macbeth. If, on the one hand, King Duncan is too gentle and Macbeth, on the other hand, is a tyrant when he becomes king, then is the play calling for something in between – a king that rules with authority and temperance? Check out our discussion of "Power" for more on this.