What role does Aeneas' destiny play in the book? What is that destiny?
Aeneas' ultimate destiny is the foundation of Rome, not directly by himself but through his descendants. Aeneas' role is to lead a band of refugees from the doomed city of Troy to a new homeland somewhere in the west, Italy as it turns out, and to establish them there. The Aeneid ends with the killing of the major obstacle to this destiny in Italy, Turnus, and although the story stops rather abruptly at this point, we know from previous references and prophecies that Aeneas' followers will establish their homeland in Italy, which will lead eventually to the foundation of a major new power, Rome.
The Romans traditionally traced their origins to Troy - Julius Caesar's family claimed its origin in Aeneas' son Iulus - possibly because of a psychological need to distinguish themselves historically from the Greeks, who were rising to Mediterranean dominance as Rome was struggling to make its way in the world in the fifth and fourth centuries BC. There is very little evidence for the Aeneas link - and of course none at all for the belief that his destiny was divinely driven through Venus and Jupiter - but this was the story that formed the basis of Rome's great national epic, the Aeneid. Aeneas himself embodies virtues that the Romans admired and regarded as essential to them: loyalty, devotion to duty, steadfastness in the face of adversity, manly courage, scorn for luxury and soft living, patriotism, even (dare we say) a kind of dullness.