What predictions do the witches make about Banquo's future in "Macbeth"?
In Act 1, Scene 3, the Weird Sisters make what appear to be grand prophecies for Macbeth. However, what they predict for Banquo will, in time, end up being even greater. In fact, that is exactly what they tell him. After they have offered their "prophecies" to Macbeth, Banquo states
[...]My noble partner
You greet with present grace and great prediction
Of noble having and of royal hope,
That he seems rapt withal. To me you speak not.
If you can look into the seeds of time
And say which grain will grow and which will not,
Speak, then, to me, who neither beg nor fear
Your favors nor your hate. (57-64)
To this, the witches respond that Banquo will be
Lesser than Macbeth, and greater.
Not so happy, yet much happier.
Thou shalt get kings, though thou be none. (68-70)
Here the witches speak in apparent paradoxes. How can Banquo be both lesser and greater than Macbeth, or not as happy yet happier? The answer lies within the final statement, and Macbeth himself helps to clarify these prophecies shortly after, saying to Banquo "Your children shall be kings" (89).
The true prophecy for Banquo is that his descendants will be kings. Banquo himself will not enjoy the fruits of the kingship, but his line will be long established as rulers. To someone such as Banquo, this is actually better than being king himself. Banquo is a good man. Unlike Macbeth, he doesn't desire power or glory for himself, but he unselfishly wants his children to have a better life. This is why, even though he will be "lesser" than Macbeth (who will become king through regicide), he will be greater. Banquo will die an honest man and be remembered as such. He won't be as happy as Macbeth the king, but because Macbeth's rule brings with it treachery, paranoia, and eventually death, Banquo will be much happier.
The Weird Sisters speak in riddles throughout the play; it is one of the greatest aspects of their characters. Through them, Shakespeare lays the groundwork for a deeper understanding of the themes and motifs at work in the play, and as deceitful as they appear to be, they actually speak a great deal of truth.
The witches predictions foreshadow future events and also present a stance with the fate vs. free will debate. While the witches cannot force Macbeth or Banquo to do anything, they can manipulate their beliefs, thus indirectly influencing their actions.
As stated in the Enotes summary section of Macbeth, the witches specifically say that Banquo "will be lesser and greater than Macbeth; even though he will never be king, his sons will." Banquo is perplexed by this at first and then considers it more deeply once he sees one of Macbeth's prophecies come true. Because his sons are not directly in line for throne, conisder the different scenarios in which this prophecy would come true in order to interpret the above quote.