Macbeth has Banquo murdered because he knows that he is suspicious that Macbeth might have killed Duncan. He also was told by the witches that Banqo’s sons would be king. This is the reason why he kills Fleance as well.
Even though Macbeth kills Duncan and takes the throne, he does not feel peace. He is worried that he will be suspected, and that Banquo knows too much. Remember, Banquo was there when the witches made their prophecy about Macbeth being king, and they also made their prophecy about Banqo’s sons being king.
Our fears in Banquo
Stick deep, and in his royalty of nature
Reigns that which would be fear'd. (Act 3, Scene 1, enotes etext p. 42).
Macbeth considers Banquo a threat because the witches said his sons would be kings. This annoys Macbeth, who says “they placed a fruitless crown” upon his head.
Macbeth makes sure the murders know Banquo is their enemy.
So is he mine, and in such bloody distance
That every minute of his being thrusts
Against my near'st of life: (Act 3, Scene 1, p. 44)
Macbeth cannot kill Banquo and Fleance himself, because they are friends and they have friends in common. So he hires the murders to do it. After all, to Macbeth“to be thus is nothing/But to be safely thus” (p. 42). In other words, what is the point of being king unless he is safe from enemies and potential enemies?
Macbeth has heard the witches' prophecies, and since their prophecies about him have all come true, he fears that Banquo's prophecy will also come true. Therefore, Macbeth perceives Banquo and his offspring as threats to his retention of the crown.
Macbeth has ignored Banquo's warning:
...the instruments of darkness tell us truths,
Win us with honest trifles, to betray's
In deepest confidence (1.3.133-135)
He also has trusted in little things that the witches have predicted, although they have hidden larger and more dangerous changes from him. Macbeth now believes that he can put confidence in the predictions of the witches.
This fatal confidence in the preternatural takes Macbeth into a dimension of the imagination that leads down a bloody and destructive path. In his developing paranoia, Macbeth feels that he must eliminate anyone who prevents his kingship.
....There is none but he
Whose being I do fear: and under him
My genius is rebuked. (3.1.57-59)
Because Macbeth perceives Banquo as a threat to his position as king, he sends for his henchmen and gives them the order to kill Banquo and his son Fleance. And so "blood will have blood."