A major part of it was certainly a method of propagating Rome and Augustus. Homer's epics were commonplace, but Augustus was disturbed that the world's most powerful state lacked an epic story. So he commissioned Virgil to remedy that issue. Nationalism was crucial during this transition period from Republic to empire, as Augustus needed to solidify rule (remember this is directly after civil war after the Second Triumvirate and several others prior to Augstus' reign.) Nationalism was a major key of allowing Augustus to consolidate rule and establish the Pax Romana

In the Aeneid Virgil depicts the Greeks as the bitter enemy of the Romans. As seen in Book 2, Troy's fall, Pyyrhus (son of Achilles) rampages through Priam's palace, and is described by Aeneas as "lusting for slaughter." The dude kills Priam's son before his eyes, then savagely drags Priam (who nobly took up arms) through his son's blood and stabs him. This is of course very different from the Iliad's depiction, where the Greeks are the heroes and the Trojans such as Paris, Hector, and Priam are seen as sort of wusses.

So, Virgil is deliberately making the Greeks out as savages and monsters, and that Aeneas barely escaped from the skin of his teeth to found Rome. It tells the Romans that Rome arose from Troy's ashes and became the worlds greatest empire. It was Rome's humble beginning. Eventually the state would grow so powerful that it would conquer the Greeks, there bitter enemies.

So, there is clearly a tension between the Romans and Greeks being depicted here. The Romans were indeed one upping the Greeks by implying that while these 'brutal monsters' were once their bullies, the Romans had the last laugh by the time of the Aeneid's commission.

In addition, a major component and reason the Aeneid was written was to propagate Augustus himself. Remember what happened to his grand uncle and adopted father Julius for becoming to power hungry and megalomaniacal. Augustus wanted the power, but he didn't want to arrive at the same fate. Thus, Augustus often gained power indirectly and sneakily as to not compromise his relationship with the people or senators. An example of this would be an act he made in senate after defeating Antony at Actium, he gave all of his power back. The Senate (being filled with his own men and knowing that another power struggle could arise if this was accepted) returned Augustus' power, and also gave him control of the military. So by pretending to be humble, Augustus acquired more power than he had before.

To consolidate rule with the people he used propaganda. The Aeneid is a good example of this, especially Book VI. After travelling through the underworld Aeneas meets his passed father Anchises, who tells Aeneas of his descendants and their accomplishments. Special attention is given to Augustus, who is stated the be "Son of gods" (Julius Caesar was deified at this point), that "even the Caspian sea trembles at the oracles that foretell his coming" and that he will establish a golden age among other things.

So ultimately Augustus is the one who commissioned Virgil to write the Aeneid, and he uses it as a method to elevate himself and the Romans. Trumping the Greeks was a major influence, but other factors should also be considered such as Augstan propaganda. With Augustus' consolidation of power and nationalism among the people partly through the Aeneid, as well as policy and infrastructural changes, Augustus prevented civil war for most of the coming two hundred years in what is known as the Pax Romana.