"Not of woman born" means born by Caesarean section.
Hecate, the head of the witches, gets angry at the three witches who prophesied to Macbeth in act 1. She is angry that they acted without permission, but she also thinks it is wrong to try to do any kindnesses for men. She says this is never appreciated or repaid. She wants the witches, in the future, to mislead Macbeth.
Therefore, when Macbeth, having no one left to turn to, asks the witches about the outcome of his battle with Macduff, they deliberately mislead him with false assurances. Macbeth takes heart from their utterance that no man born of a woman can kill him, as he interprets this to mean he will survive the battle.
The witches are playing with words. Of course, Macduff comes from a female womb. However, rather than being pushed down the birth canal, Macduff is, for some reason, delivered by C-section.
Macbeth finds out too late he has been deceived. Macduff will kill him. However, as Macbeth reveals in a late soliloquy, he is tired of life, which has disappointed him, so in a sense he is not sorry to die. He has also been a tyrant, more concerned about keeping power than helping his people, so his death offers Scotland a new beginning.
Macbeth is greatly relieved when one of the spirits the three witches have summoned tells him that he should be "resolute" because "none of woman born" will ever be able to harm him. For Macbeth, this is an opportunity to heave a huge sigh of relief, because, as far as he understands it, all people are born from women. He interprets this statement to mean that absolutely nobody alive will ever be able to harm him, because he cannot imagine what sort of person might not have been born of a woman.
Unfortunately, however, there is a nuance in the statement which does not occur to Macbeth. The apparition actually means that nobody who has been born through the natural process of labor and birth will be able to harm Macbeth. Actually, as Macbeth finds out to his detriment, Macduff is able to harm him. Macduff was not born from his mother in the natural way at the appropriate time but was "untimely ripped" from her womb, in what we would today classify as a C-section birth. As such, he is not covered under the terms of the apparition's prophecy and is able to put an end to Macbeth's tyrannical reign.
In act 4, scene 1, Macbeth meets with the Three Witches to question them further about their prophecies in hopes of learning more about his future. However, the Three Witches offer Macbeth several enigmatic prophecies, which make him overconfident and lead to his downfall. The second apparition that the Three Witches summon is a bloody child, who tells Macbeth,
"Be bloody, bold, and resolute. Laugh to scorn The power of man, for none of woman born Shall harm Macbeth." (4.1.81-83)
Macbeth misinterprets this prophecy to mean that no man will ever be capable of harming him since every man is born from a woman. However, the second prophecy does not include men who were born by Caesarean sections. In the Middle Ages, Caesarean sections were considered rare and unnatural, which is why Macbeth overlooks this exception.
Later on in the play, Macbeth comes face to face with Macduff during the final battle. In act 5, scene 8, Macduff tells Macbeth,
"Despair thy charm, And let the angel whom thou still hast served Tell thee, Macduff was from his mother’s womb Untimely ripped." (5.8.13-16)
Essentially, Macduff discloses the fact that his mother birthed him by Caesarean section, which means that he was not "born from a woman" as the prophecy stated. Macduff then kills Macbeth and Malcolm becomes the King of Scotland.
You are of course refering to the prophecies that the witches give Macbeth in Act IV scene 1 when he returns once again to their lair, demanding to know the truth of his fate. The prophecies he receives are typically obfuscated and unclear so that Macbeth is left to draw his own conclusions and is unsure of their precise meaning. Note the prophecy that the Second Apparition gives him in this scene:
Be bloody, bold and resolute: laugh to scorn
The power of man, for none of woman born
Shall harm Macbeth.
Ironically, the apparition goads Macbeth on into ever-further acts of violence with the false hope that nobody who is born of woman can harm him. Macbeth himself interprets this by thinking that he is invincible, as he says he has no need to fear Macduff. Of course it is only in Act V scene 8 that Macbeth learns the truth. As he tells Macduff that he is invincible because nobody who was borne of woman can kill him, Macduff replies revealing the true meaning of teh apparitions words:
Despair thy charm;
And let the Angel, whom thou still hast serv'd,
Tell thee, Macduff was from his mother's womb
Therefore the prophecy refers to someone who was born by cesarian, where the mother's stomach is cut open and the baby is pulled through that way, rather than borne in the normal method. Macbeth's misinterpretation of this prophecy leads to his over-confidence and his doom.