The act opens with an important metaphor inspired by the witches' prediction in Act 1. Banquo, by this point in the play, has begun to believe Macbeth has achieved his kingship wrongfully, and he is still trying to understand the implications of the witches' prediction that he, not Macbeth, will father Scotland's future kings:
But that myself should be the/root and father/Of many kings. (III:4-6)
Banquo, still puzzled by the witches' comments, refers to himself as the "root" of Scotland's future kings--Banquo compares himself to the root of a tree, a common, but appropriate, metaphor for the foundation of a dynasty.
Throughout the opening lines of Act 3, Scene 1, the witches' predictions continue to bother Macbeth, in part because they imply Macbeth will die childless, and he frames this problem in a subtle metaphor:
Upon my head they placed a/fruitless crown/And put a barren sceptre in my/ gripe,/Thence to be wrench'd with an/unlineal hand. . . . (III.1:64-69)
The controlling metaphor uses the language of childlessness: the "fruitless crown" signifies Macbeth's kingship, but with no children to inherit his kingdom, and a "barren sceptre" continues the theme of Macbeth's inability to create a dynasty. Both crown and sceptre are symbols of kingship and power, but they are meaningless if there are no children to carry the dynasty forward. Macbeth's last comment encapsulates his greatest fear--that his kingship will be usurped by an unlineal hand, that is, by someone not related to Macbeth. Unlineal hand is a good example of the rhetorical device known as synecdoche, that is, using a part to represent the whole. In this case, the hand represents the person who will take Macbeth's kingship by force.
Macbeth concludes this interior monologue with a metaphor symbolizing the inevitable struggle he sees with Banquo:
Rather than so, come, Fate, into/the list,/And champion me to the/utterance!
During the period in which the play takes place, everyone, especially royalty, would understand this metaphor to be based on jousting--an activity that was both practical as preparation for war and recreational. Macbeth here envisions himself jousting with Banquo, or Banquo's heirs, with Fate as his lady-luck. Macbeth also uses a word--utterance--that means, in this context, the bitter end, so he does not expect this struggle for his kingship to be easy or, more important, necessarily successful.
Shakespeare's metaphorical language in the opening of Act III, which centers on dynastic concerns for both Banquo and Macbeth, allows us to understand what is uppermost in their minds. More important, the metaphorical language points to the way in which the characters look at their world. In Macbeth's case, he perceives the violence with which he will defend his kingship and, equally important, the enemies he faces--his inability to produce heirs and Banquo.