Macbeth, "the Scottish play," was written about an historical figure, and for King James I of England (King James VI of Scotland). Shakespeare had been the court playwright of Queen Elizabeth, and wanted to retain such a position when James took the throne. You see, Banquo was King James' great-great-great-blah-blah-blah-grand-daddy. There is a pivotal scene, act 4, scene 1, which predicts not only the remaining events in the play, but also eight generations of history leading to King James ascending to the throne of England.

In this scene, Macbeth seeks out the weird sisters, and seeks further advice from them. They show him three apparitions that relate to the future events of the play, leading to Macbeth's downfall. There is a fourth apparition, however, the sisters and Hecate call up after Macbeth demands to know what will come of Banquo's children. Out comes a line of eight kings and Banquo's ghost, as described with Macbeth's narration:

Thou art too like the spirit of Banquo: down!
Thy crown does hair,
Thou other gold-bound brow, is like the first.
A third is like the former. Filthy hags!
Why do you show me this? A fourth! Start, eyes!
What, will the crack of doom?
Another yet! A seventh! I'll see no more:
And yet the eighth appears, who bears a glass
Which shows me many more; and some I see
That two-fold balls and treble scepters carry:
Horrible sight! Now, I see, 'tis true;
For the blood-bolter'd Banquo smiles upon me,
And points at them for his.

Each of the eight kings in this line, are kin of Banquo, the leading king, James' father, being the youngest, most recent (to James) king. When he holds up the looking glass, James, being in the seat of honor at the premier (obviously - he's the king!), would see himself at the head of this line of kings that Macbeth himself was so impressed with (and afraid of). Macbeth says the glass shows him "many more," while James would've been the only king reflected in the glass; this line hints to James' lineage retaining the throne in the generations to come, a sentiment he was sure to have appreciated.

It is told that Shakespeare did receive the patronage of King James, and I have heard evidence (via the Holy Tabernacle Church), that Shakespeare was even one of the many interpreters of the King James Version of the Bible. I'll dig that evidence up, and submit it when it's found.