Macbeth's conflict with Macduff emerges after the murder of Duncan, when Macduff eventually becomes suspicious of Macbeth. We first see this suspicion, or at least some uneasiness with the new king, when he announces that he will return to Fife rather than attending Macbeth's coronation. He says that Donalbain and Malcolm are suspects, but has no desire to see the new king crowned. After the witches tell him to beware of the thane of Fife, he has Macduff's family murdered, setting up the dramatic final battle between the two, from which Macduff emerges victorious, holding Macbeth's severed head.
In fact, it is Macduff who affects the final resolution between Macbeth and the supernatural. He informs the king that he was born by caesarian section, thus fulfilling the supernatural prophecy that claimed Macbeth could only die at the hands of one not of woman born:
Despair thy charm; and let the angel whom thou still hast serv'd tell thee, Macduff was from his mother's womb untimely ripp'd.
Another element of supernatural sanction for Macbeth's demise emerges when he is told that Macduff's attacking army advances camoflaged by branches from Birnam Wood, which confirms another prophecy that Macbeth should not fear anyone until Birnam Wood advances on Dunsinane. Obviously, this conclusion frames the story which began with the prophecy that Macbeth would be King of Scotland, and indeed we see an element of the supernatural at the king's banquet, as Macbeth is tormented by Banquo's ghost. Macduff both brings about some measure of justice and serves as a human instrument of the supernatural.