Why would people in Shakespeare's time have found the story of "Macbeth," which was about events that occurred centuries earlier, relevant to their own concerns?

There are two main reasons why Macbeth might have resonated with the audience at the time. First, because of the political situation of the 17th century, and second, because of the universal themes that the play addresses.

Macbeth was relevant to the politics of the time because the ruler of England was James I, who was previously James VI of Scotland. Macbeth's setting is also Scottish, and the link between Banquo and royalty is intended to link the king James I to the story (as descendant of Banquo). Moreover, the story of legitimate kingship defeating illegitimate kingship was intended to provide support to the reign of James I.

In terms of universal themes, the play touches on many subjects that humans have found relevant throughout time. For example, the play warns of the dangers of uncontrolled ambition. It also shows that people receive punishment for their bad deeds. Finally, it emphasizes the idea that people cannot escape their own destiny.