Macbeth wanted Banquo to die because one of the three witches told Banquo that his sons would be kings, and that includes Fleance.
The third witch said, earlier on in the play, to Banquo, "Thou shalt get kings, though thou be none."
So if Fleance or his future brothers or sons became kings, then Macbeth would lose his position on the throne.
Macbeth found his chance to tell the murderers to kill Banquo as he won't return by nightfall, and they could also kill Fleance, which is why Macbeth asks Banquo, "Goes Fleance with you?" to assure himself that Fleance dies as well.
However, Fleance manages to escape but Banquo dies, which stills troubled Macbeth.
(I hope this helps)