In Act 3, Scene 1 Macbeth has a long soliloquy beginning:
To be thus is nothing,
But to be safely thus. Our fears in Banquo
Stick deep, and in his royalty of nature
Reigns that which would be feared.
What troubles him the most is that the three witches prophesied that Banquo's descendants would be kings and not his own sons. Macbeth believes that this is predetermined by fate but that he can actually defy fate with his free will by murdering Banquo and his son Fleance. If he can manage to accomplish that, he can cut off Banquo's line completely. He is opposing his free will to fate itself. In the final lines of the soliloquy he says:
They hailed him father to a line of kings.
Upon my head they placed a fruitless crown
And put a barren scepter in my grip,
Thence to be wrenched with an unlineal hand,
No son of mine succeeding. If 't be so,
For Banquo's issue have I filed [defiled] my mind,
For them the gracious Duncan have I murdered,
Put rancors in the vessel of my peace
Only for them, and mine eternal jewel
Given to the common enemy of man [Satan]
To make them kings, the seeds of Banquo kings.
Rather than so, come fate into the list,
And champion me to th' utterance.
He challenges fate to come--metaphorically--into the arena for a trial by combat and fight him [champion him] to the death [to th' utterance]. It turns out that fate wins the trial by combat, because Banquo is killed but Fleance escapes.