Now that Macbeth has fulfilled the prophecy of the witches and succeeded in his own ambition to become king of Scotland by murdering King Duncan and taking the crown, Macbeth remembers that there is another prophecy that needs to be addressed, which is the prophecy that the witches made to Banquo, "Thou shalt get [beget] kings, though thou be none" (1.3.70)
This is an issue which Banquo himself raises at the very beginning of act 3, scene 1, almost immediately after Macbeth has been crowned king. In his opening lines in the scene, Banquo notes that the prophecy that the witches made to Macbeth has come true, but he suspects that Macbeth "play'dst most foully for't" (3.1.3)—that is, that that Macbeth killed Duncan to become king.
Interestingly, though, Banquo starts to think about the possibility that if the prophecy to Macbeth came true, might not the prophecy that the witches made to him also come true.
Military strategist that he is, Macbeth is once step ahead of any such eventuality. Macbeth is already planning to thwart that prophecy by murdering Banquo and Banquo's son, Fleance. In his soliloquy, Macbeth explains his reasoning for wanting to kill them and essentially tries to justify their murders, at least to himself.
"To be thus," meaning to be King, "is nothing" (3.1.52), Macbeth says, unless he feels safe on the throne, which is something he can't feel as long as Banquo and Fleance are alive. Macbeth believes that if Banquo wanted to be King, or wanted his children to be kings, then Banquo has the temperament, the wisdom, the courage, and the ability to accomplish those goals.
In a way, Macbeth acknowledges that Banquo is smarter than he is: "Under him my genius is rebuked" (3.1.59–60), and Macbeth fears that he can never be safe on the throne or rule effectively as king until he rids himself of Banquo and Fleance. Macbeth doesn't want his efforts to murder Duncan and put himself on the throne to be in vain by simply facilitating the prophecy that Banquo's descendants will become kings.
MACBETH. For Banquo's issue have I filed my mind,
For them the gracious Duncan have I murdered, (70)
...To make them kings, the seed of Banquo kings! (3.1.69–70, 74)
In order to avoid that possibility, Macbeth decides to do whatever it takes to stay safely on the throne, and through the deaths of Banquo and Fleance, he intends to take the weight of the prophecy and the fear of its consequences off his mind.
As fate—and Shakespeare's knack for plotting his plays—would have it, the murderers that Macbeth summoned to kill Banquo and Fleance are waiting to speak with him at that very moment.