In Act 5 of the play 'Macbeth' by William Shakespeare, Macbeth is set upon going down fighting with the witches' words about not being defaeated by a man born of woman ringing in his ears. It is almost as if he sees the likely outcome but thinks as he can't see a way out, he will fight anyway and see what happens to make the witches' prophecy come true. Then follows a series of fast action packed images of the fighting and the violence. Then, realising he has been tricked by the double-entendres of the witches and that in fact he can be killed as Macduff does not after all fit the 'born of woman' description, he can't stand the idea of being second to Macduff and the thought of being humiliated. He goes on - and is slain and beheaded.
In Shakespeare's Macbeth, the fight between Macbeth and Macduff occurs in Act 5, Scene 8. The confrontation begins when Macduff calls to Macbeth: "Turn, hellhound, turn!"
Macbeth still, at least partially, believes he cannot be defeated by Macduff because, as the witches predicted, Macbeth cannot be killed by a man born of woman. I say "at least partially," because the rational side of Macbeth knows his situation is hopeless. He feels nihilistic after his wife dies (The "Tomorrow" speech), and he feels like a baited bear, a bear chained to a tree and attacked by dogs for the enjoyment of an audience. He has also seen Birnam Wood move. Rationally, he knows he is doomed.
He begins the fight with Macduff, however, still holding on to the idea that he can't be defeated. After all, he has just killed Young Siward with relatively little trouble.
After listening to Macbeth brag of his charmed life, though, Macduff informs Macbeth that he was not born of woman (Macduff's mother died in childbirth before Macduff was born, so, technically, Macduff was born of a body, not of a woman).
Nevertheless, Macbeth faces Macduff and fights nobly. The fight moves offstage, and the result is not known until minutes later, when Macduff enters the stage carrying Macbeth's head.
Macbeth is thus killed, and Scotland is cleansed from evil.
This fight occurs at the very end of the play. In fact, it is just about the last action that happens at all. The outcome of the fight is that Macduff kills Macbeth. He takes him offstage, then cuts off his head and brings it to show to Malcolm, who will now reclaim his rightful place as King of Scotland.
Although Macbeth has been the bad guy in this play, at least he dies well, telling Macduff that he doesn't care if the prophecies have been fulfilled -- he is going to fight to the bitter end.
You have got some beautiful answers. Yet, I'll add few more lines of my own.
The outcome of the fight between Macbeth and Macduff in 5.7 can be interpreted from three different angles, and they are as follows:
1. Disillusionment of Macbeth: In this final scene, Macbeth realises what was his fault, and understands that the witches did not anything but equivocating. When Macduff informs about himself while attacking Macbeth that he is born of his dead mother via surgery, Macbeth is disillusioned finally. All his hopes left rest get shattered.
2. Restoration of harmony in Scotland: By killing the butcher-like Macbeth, peace is restored at last in Scotland. The end of the tyrant brings harmony to the country.
3. Good's victory over evil: The termination of the brutal tyrant shows the power of good. It proves that, ultimately, evil can not be spared, and good defeats the evil at the end.
Despite these aspects, we also notice Macbeth's heroic superiority in this scene, though it has not been that much highlighted. He says to Macduff: "I will not yield... I will try the last..." though he knows well that his death is certain. Here, he has acted definitely like a brave and valiant warrior by not giving up till the end.