The witches' first prophecy is what causes Macbeth to think that he could be king to begin with. There is no indication that he had that ambition before they spoke to him. The witches demonstrate that they can tell the future by predicting that he will become Thane of Cawdor, which immediately takes place. This experience makes Macbeth believe that he is fated to become the king, but, of course, he is not entirely content just to let that happen without acting. With some spurring from Lady Macbeth, he murders Duncan. But that is not enough for Macbeth; the witches also predicted that Banquo's children would be kings, implying that at some point Macbeth's line would die out and Banquo's line would rule instead. Macbeth then has to have Banquo killed too.
The witches prompt every murder that Macbeth commits or commissions following the murder of King Duncan. He visits the witches again in act 4, scene 1. They tell him to "beware the Thane of Fife! Beware MacDuff!" This prophecy results in Macbeth having MacDuff's family murdered when he learns that MacDuff has fled to England, out of his reach for the present. The witches' prophecies make Macbeth commit multiple murders in order to try to secure his future power and safety. However, they also cause him to believe that he is secure, telling him that "none of woman born can harm Macbeth." This prophecy turns out to be a trick because MacDuff was born by C-section, rather than through labor, so he does not count as being "born of woman" and can kill Macbeth. The witches play with both Macbeth's ambitions and his fears at once.
The witches' prophecies are important because without them, Macbeth would have had no reason to kill Duncan. Planting the idea in Macbeth's head is what makes the events of the play happen: no prophecies, no play. They also spur the plot onward once it is in motion, prompting more and more killing until Macbeth is finally utterly destroyed.