In Act IV, Scene 1, the apparitions warn Macbeth to be careful of Macduff, but also maintain that "none of woman born/ Shall harm Macbeth."
Macbeth is happy to hear this, but soon decides he will rid himself of Macduff anyway, just to ensure his chances of maintaining his hold on power. He soon discovers Macduff has fled England, and is miffed he didn't act sooner. To ensure no heirs follow Macduff, he orders Macduff's wife and children to be killed.
The castle of Macduff I will surprise,
Seize upon Fife, give to th' edge o' th' sword
His wife, his babes, and all unfortunate souls
That trace him in his line.
In Act V, Scene 7, Macbeth kills young Siward
and proclaims he wasn't afraid to face the warrior because Siward was born of a woman. In Act V, Scene 8, Macbeth initially refuses to fight Macduff; he claims he's killed enough of Macduff's family members and wants to refrain from killing Macduff, too. Furthermore, Macbeth argues that he leads "a charmèd life, which must not yield/ To one of woman born."
At this point, Macbeth doesn't make any moves to kill Macduff because he thinks Macduff is no threat to him. It is only after Macduff asserts that he was "untimely ripped" from his mother's womb that Macbeth begins to take his challenger seriously.
So, it's significant that Macbeth doesn't initially manage to kill Macduff. Earlier in the play, Macduff escaped Macbeth's clutches when he fled England. Later, on the battlefield, Macbeth initially refuses to engage Macduff. He's only forced to fight Macduff when Macduff corners him. In the end, Macduff beheads Macbeth and proclaims Malcolm
king of Scotland. In the play, Macduff fills his role as the one man who can kill Macbeth; his character fulfills the earlier prophecy that Macbeth should both beware of Macduff and be wary of the man who is not "born from a woman."