Banquo had a son named Fleance that Macbeth feared would be king, he suspected that Macbeth killed King Duncan, and he was killed by Macbeth’s murderers.
Banquo was there when Macbeth heard the witches' prophecies related to his kingship, Banquo’s sons being king, and Macbeth’s promotion to Thane of Cawdor. Therefore, Macbeth was pretty sure that Banquo was aware that he killed the king or at least suspected him of it. Indeed, Banquo says as much in his soliloquy at the beginning of Act 3, Scene 1.
In a soliloquy, Macbeth explains that he is worried about Banquo.
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 fear'd: 'tis much he dares;
And, to that dauntless temper of his mind,
He hath a wisdom that doth guide his valour
To act in safety. (Act 2, Scene 1)
There are two reasons to fear Banquo. The witches told Banquo, “Thou shalt get kings, though thou be none,” which means that he will not be king but that his sons will be king. This is not good news. For that reason, Macbeth has to kill both Banquo and Fleance.
After making sure he knew where they would be, Macbeth sent three murderers after Macbeth and Fleance, to make sure they were killed before the banquet he kept insisting Banquo attend.
Fleance his son, that keeps him company,
Whose absence is no less material to me
Than is his father's, must embrace the fate
Of that dark hour. Resolve yourselves apart:
I'll come to you anon. (Act 3, Scene 1)
The murderers are able to successfully kill Banquo, but Fleance gets away. I suppose it is possible that the prophecy could come true. Fleance or his sons could eventually become king. Banquo did attend the banquet, but he came as a ghost--not invited!