Macbeth organises the assassination of Banquo and Fleance in order that he will retain the throne on Duncan's death. However, he has more than one obstacle in his way.
Macbeth is perturbed when Malcolm, King Duncan's son, is proclaimed Prince of Cumberland in Act I scene iv -
The Prince of Cumberland! That is a step
On which I must fall down, or else o'erleap,
For in my way it lies.
The title of Prince of Cumberland is akin to the current UK title of Prince of Wales, that is, official heir to the throne. Of course Macbeth does not wish a named heir to stand in his way, so wishes Malcolm dead. As Malcolm flees, this plan is temporarily suspended.
He is, however, most wary of his great friend Banquo, as the prophesies delivered by the witches in Act I Scene iii suggest that he is more of a threat to Macbeth -
Thou shalt get kings, though thou be none.
So all hail, Macbeth and Banquo!
However, as well as Banquo's death, Macbeth requires Banquo's progeny to be killed also. This is Macbeth's third target; Banquo's son, Fleance. Their deaths would render the prophesy untrue.
The audience would probably know that it was Banquo's line which did in fact take the throne, so would know that Macbeth's wicked plans would be thwarted somehow.