The witches want to meet with Macbeth in order to plant the seed of kingship in a brain already full of ambition. The witches are not definite in their reasoning the first time the reader hears them speak; however, they give a clue as to their purpose in the following lines: "Fair is foul, and foul is fair. / Hover through the fog and filthy air" (1.1.10-11). Macbeth (we assume) has never had the gall enough to usurp the throne from Duncan. Therefore, when the witches arrive and make a prediction the question arises whether they are putting a new idea in his head or whether they are simply fueling the fire of Macbeth's ambition making it that very "vaulting ambition" that Macbeth has become so famous for. In my opinion, it can be true and supported through evidence either way. That is the beauty and the ambiguity of Shakespeare's genius.
William Shakespeare's The Tragedy of Macbeth could have worked just fine without the contrivance of witches. After all, the witches serve primarily to influence the Scottish general Macbeth's thinking by prophesying that this military hero will one day be king. Less extravagant means could have been used to propel the character of Macbeth along his trajectory, but it has been suggested that the playwright was influenced by King James, who apparently did believe in witches and witchcraft and who was an inspiration for this particular play.
Macbeth opens with the scene of the three witches clearly planning on another gathering in the not-too-distant future, and with the purpose of encountering Macbeth:
First Witch: When shall we three meet again? In thunder, lightning, or in rain?
Second Witch: When the hurly-burly’s done, When the battle’s lost and won.
Third Witch: That will be ere the set of sun.
First Witch: Where the place?
Second Witch. Upon the heath.
Third Witch: There to meet with Macbeth.
Shakespeare begins his tragedy with these three sorcerers agreeing to meet following a conflict in which Macbeth and Banquo, two prominent noblemen of Scotland, played important roles. They know from whence these two generals and friends approach, and they intend to sow discord and provoke Macbeth to destroy himself through unbridled ambition. They do this by "predicting" that Macbeth will become a king, and that Banquo's sons will also become kings, thereby pitting these close allies against each other. Note in the following passage the murky way in which the witches prophesy these two generals' futures:
First Witch: Lesser than Macbeth, and greater.
Second Witch: Not so happy, yet much happier.
Third Witch: Thou shalt get kings, though thou be none: So all hail, Macbeth and Banquo!
First Witch: Banquo and Macbeth, all hail!
The witches are deliberately instilling in Macbeth, an already ambitious man, a sense of future greatness exceeding the levels he has already attained, and he takes the bait. The witches, by their prophecies, have set into motion the chain of events that makes Shakespeare's play one of his most admired tragedies. Before the play ends, Macbeth will engineer the deaths of all those near to him and, ultimately, his own. The witches arrange their encounter with him for the purpose of bringing about his and the kingdom's doom.