Final answer:
The "show of kings" is significant as it prophesies a lineage of kings descending from Banquo, foretelling Macbeth's futile attempt to establish his own legacy and indirectly legitimizing the rule of King James I. This contributes to the play's themes of fate, ambition, and prophecy.
Step-by-step explanation:
The "show of kings" that the witches conjure for Macbeth is significant because it provides a series of prophecies that establish the future lineage of Scottish kings, directly connecting Macbeth's actions to the historical legacy of Scotland. This spectral procession reveals to Macbeth that Banquo's descendants will inherit the throne, leaving Macbeth with the knowledge that his efforts to secure the throne for his own lineage are in vain. The sequence ends with the apparition of a mirror reflecting an endless line of kings, implying that Banquo's progeny will reign for many generations. This is historically significant as it ties to the idea of the divine right of kings and the Stuart dynasty, which was ruling at the time Shakespeare wrote the play. Hence, the play indirectly legitimizes King James I's claim to the throne, presenting it as a fulfillment of a prophetic lineage.
These apparitions, offering a mix of truths and half-truths, suggest themes of fate, ambition, and the nature of prophecy, contributing to Macbeth's eventual downfall. They serve to underline the futility of Macbeth's actions in attempting to control his destiny while highlighting the natural order and legitimate lineage over usurpation. The entire episode casts doubt on the reliability of the witches and their prophecies, contributing to the play's exploration of deception, equivocation, and free will.