The witches' predictions play a large role in Shakespeare's Macbeth. They are, of course, what lure Macbeth (and Lady Macbeth) in murdering Duncan in the first place. However, as Macbeth becomes more paranoid, he seeks out the witches again for a new set of predictions.
There are several important elements here that lead directly to Macbeth's downfall. Banquo has already asked...
What, can the devil speak true? (I.iii.113)
The Elizabethans thought it was impossible for the devil to tell the truth. What is Macbeth thinking in believing anything that the servants of a darker power tell him? Secondly, he believes he can order them about—what, a mere mortal, trying to give orders to the devil's servants? Again, this is foolishness on Macbeth's part—he is partly blinded by his ambition and partly by his own elevated sense of power. Finally, Hecate has already made arrangements for this next set of predictions to trick Macbeth into delivering himself into circumstances that will lead to his destruction—by appealing to the false sense of security that the second set of prophecies will create in Macbeth.
The first apparition that accompanies the first prediction in Act Four is the hardest (I think) to understand. I see this as a "throw away" line—something that really isn't that important. With the first set of predictions (in Act One), the Weird Sisters greeted Macbeth by his name: this was meaningless, except to perhaps give him the sense that they had the power to magically know who he was. With this new set of predictions, they do the same: Macbeth already knows he has to be careful of Macduff.
The armed head refers to Macduff as a soldier, a worthy opponent—the man who will end his life (though he has no idea of this by seeing the apparition).
This apparition foreshadows Macduff's leading role in the attack on Macbeth, and perhaps also Macbeth's beheading by Macduff.
Perhaps the apparition is something that Macbeth ignores, as he seems not to understand or be too worried about the second and third apparitions either. Macbeth hears and sees what he wants to hear and see. This is where the witches begin to tighten the noose around Macbeth's neck.