In this soliloquy Macbeth reveals both his insecurity that he will be able to retain his awfully gained throne and his bitterness when he realizes that the prophecy which favored his own ascendancy also predicted that the issue of Banquo, a much more worthy man, will gain the throne that Macbeth gives up his "precious jewel" (his soul) to attain for them both.
Macbeth has no living children to inherit the throne; upon his head the witches placed a "fruitless throne" (3.1.62). Banquo's children will become a "line of kings" (3.1.61).
Macbeth realizes two things: 1) He murdered Duncan for the throne which will cost him his imortal soul so that 2) Banquo (who has risked nothing) will be the father to many future kings. Macbeth also acknowledges that Banquo is daring, royal in nature, and wise in his valor--everything Macbeth is not and, therefore, a reasonable threat to his throne. Since the the prophecy will no longer benefit himself, he begins at this point to try to foil the prophecy and to secure the throne for himself by having Banquo and his son killed.
In Act III, Scene I, Macbeth is beginning to feel the effects of his newly acquired power. His attitude is one of smug satisfaction at being crowned and he is planning a banquet, which is both the high point of his time as king and the beginning of his descent into madness.
In his speech in this scene, he shares conversation with Banquo about the two murderers, referring to Malcolm and Donalbain.
"We hear our bloody cousins are be-
In England and in Ireland, not confessing
Their cruel parricide, filling their hearers"
Act III, Scene I
After dismissing Banquo, jealousy pours out of Macbeth at the fact that he has no son. He is projecting his kingdom into the future and sees nothing but Banquo's heirs on the throne.
"Upon my head they plac'd a fruitless crown,
And put a barren sceptre in my gripe,
Thence to be wrench'd with an unlineal hand,
No son of mine succeeding. If't be so,
For Banquo's issue have I fil'd my mind;
For them the gracious Duncan have I murder'd;" Act III, Scene I
He works himself into a raging fury as he interrogates two men he has summoned to kill Banquo and Fleance. The speech is particularly sad, because Macbeth is losing touch with his humanity. He is cutting ties with his very dear friend Banquo and succumbing to a false sense of power that demands he protect his crown, as if he could fend off every possible threat by murder.
Macbeth feels worry and anxiety concerning Banquo: "Our fears in Banquo stick deep." Macbeth fears Banquo's "royalty of nature"; that is, Banquo also heard the witches' predictions and Macbeth fears Banquo is too honorable of a man to follow Macbeth in his treachery. Also, the witches "hailed him [Banquo] father to a line of kings." Macbeth, then, also has another concern; he is afraid Banquo's sons will inherit the throne from him!
Macbeth ends this soliloquy angry at Banquo with the thought that he has "the gracious Duncan...murdered" for Banquo and not himself. Rationalization at its best, don't you think?
A soliloquy is the window to the heart and soul of a character. Macbeth's soliloquy in ActIII Sc.1 reveals the agitated state of his mind just before he meets the hired assasins who are to murder Banquo.
FEAR: "There is none but he/Whose being I do fear." Macbeth is frightened of Banquo because Banquo has also heard the witches' prophecies and he is afraid that Banquo suspects him of murdering Duncan. Moreover, he knows fully well that Banquo is not only a very courageous warrior but also a very cautious person: "He hath a wisdom that doth guide his valour/To act in safety." Meaning, it would be very very difficult to murder him.
JEALOUSY: Macbeth is jealous of Banquo because Macbeth is childless and the witches have prophesied that Banquo's children will become kings in the future: "Upon my head they placed a fruitless crown."
LOW SELF ESTEEM and SELF WORTH: Macbeth feels that all his efforts have gone to waste because all the troubles that he has undergone are only going to benefit Banquo's children:"For Banquo's issue have I filed my mind."
MISERABLE and GUILTY: Macbeth feels miserable and guilty that he has murdered Duncan and confesses that he has lost all his peace of mind :"Put rancours in the vessel of my peace."
After Macbeth has tormented himself with all these negative feelings he instructs the murderers not only to murder Banquo but also his son Fleance.