It is the promise of the second apparition the witches show Macbeth (Act IV, Scene 1): "no one born of woman can do harm to Macbeth." Macbeth takes it to mean that no man can kill him, and the play shows in the end that the sentence had an exception.
In the moment, Macbeth cheers up: "Then live, Macduff! What need have I to fear you?" But he decides all the same that Macduff must die, to have a guarantee from Fate.
In Act V, Scene 7, Macbeth kills young Siward and remarks: "You were born of woman." Facing Macduff, he says: "I bear a charmed life, and no man born of woman will put an end to it." Macduff answers: "Macduff was torn from his mother's womb before his time." Macbeth reacts by cursing the tongue that tells him this and the demons that "play with us in ambiguous phrases."
Before the duel, in the same scene, he had already said: "Who is the man not born of woman? He is the one I must fear, and no one else." The promise is fulfilled to the letter: Macduff was torn from his mother's womb before his time, and the prophecy does not protect Macbeth from him.