Act 3 is a very important act in terms of transition. By this time, Macbeth has been visited by the witches and urged by Lady Macbeth to kill Duncan. The king’s legitimate heirs to the throne, Malcolm and Donalbain, flee. Macbeth takes the throne, and everything should be good. He has what he wants, yet he is not able to rest.
The scene opens with Banquo’s comments that he worries Macbeth might have done something terrible in order to be king.
Thou hast it now: King, Cawdor, Glamis, all,
As the weird women promised, and I fear
Thou play'dst most foully for't: (Act 3, Scene 1, enotes pdf. p. 40)
This quote is important because it demonstrates that Macbeth cannot rest easily yet, and foreshadows trouble for him later. It also shows trouble for Banquo, and it isn’t long before Macbeth has him murdered.
Another important quote is also in Act 3, Scene 1.
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. (p. 42)
You see that Banquo is suspicious of Macbeth, and Macbeth is suspicious of Banquo. This is not the only reason why Macbeth has him killed. The witches have predicted that Banquo’s sons will be king, and Macbeth figures the easiest way to prevent that is to kill Banquo.
Lady Macbeth also has something to say about this.
Nought's had, all's spent,
Where our desire is got without content.
’Tis safer to be that which we destroy
Than by destruction dwell in doubtful joy. (Act 3, Scene 2, p. 45)
Lady Macbeth pushed her husband to kill Duncan and become king, as the witches predicted, but she wants him to stop there. Basically, she is annoyed that he can’t be happy with what he has, and she is worried that he is going to cause more trouble. Her fears are realized when Macbeth tells her “We have scotch'd the snake, not kill'd it” (p. 45). Macbeth tells her not to worry about anything, he will take care of it all.