"Beware Macduff" shows that Macduff could be the one to kill and overthrow Macbeth. He does, and this is tied in to the second apparition.
"Man not born of woman" is referring to Macduff. His mother died before he was born and he was taken from her, but she did not give birth to him. He is the one to finally defeat Mabeth. When he explains this to Macbeth as they are fighting, Macbeth sees his fate is near.
"Birnam Wood to Dunsinane" occurs when the men carry limbs and branches with them to camoflage so that Macbeth doesn't see them coming. Macbeth doesn't think that the trees will begin walking, but once they appear to be moving, he realizes his fate.
The First Apparition warns Macbeth against Macduff--'Beware of Macduff'. Macbeth is already apprehensive of the Thane of Fife and contemplates his killing. The prophetic warning thus confirms Macbeth's apprehension. Later, in Act V, Macduff beheads Macbeth and the warning comes true.
The Second Apparition, a bloody child, assures Macbeth that no man born of a woman can ever cause any harm to Macbeth. Unable to see through the equivocation, Macbeth feels relieved that Macduff can do him no harm. But later in the Fifth Act, Macduff reveals to Macbeth's disillusion that he was born untimely, and not strictly born of the mother's womb. Macbeth realises how the seemingly assuring prophecy was couched in deceptive language.
The Third Apparition, a crowned child with a tree in its hand, further assures Macbeth that he can never be vanquished until the Birnam Woods comes to the Dunsinane hill. Once again, Macbeth in his credulous over-confidence fails to see the equivocation and feels safe. In the Fifth Act, Malcolm instructs his ten thousand-strong army that each soldier should take a leafy branch from the Birnam Woods to use the same as a cover while marching towards the Dunsinane castle as a tactic of camouflage to shadow their numbers. A servant, confused and alarmed, reports to Macbeth that he has seen a 'moving grove'.