This question was asked almost exactly a year ago. Here's the responses from that thread.

I'm paraphrasing this while watching playoff basketball but my source is "The Beginnings of Rome " by T.J. Cornell.

This has as much to do with the Greeks as it does with the Romans. Greeks had the tendency to explain the origins of people with their mythology. This included people outside of the Greek world like the Romans and other Italic people. This means that Greek heroes and figures were perfect explanations for other people's origins as well. Many groups would simply accept this interpretation of their origins. There is evidence of cults of Herakles/Hercules and Aeneas in Etruscan and Roman settlements in the 6th cent BC (so 500's and probably earlier). Aeneas, the progenitor of Roman people, had a cult presence in the Latin settlement of Lavinium before it was taken by Rome in the Latin Wars. This is to say that Greek figures in Mythology were known to Italic people for some time. Greek writers toward the end of 5th cent. BC (so late 400's) had identified Rome as the possible landing place of the Trojan prince something that flattered Rome. Rome certainly liked Aeneas and elements of the story: devoted, patriotic, and origins that displayed their mixed origins. So Aeneas was well liked, Greek figures were worshiped in Italy before the rise of Rome as a leading power, and the story carried some prestige. However, why the Trojans? It allowed them to claim the prestige of being apart of the Hellenistic mythos/world while making them not Greek. There were periods of animosity between Greeks and Rome and so this allowed for Rome (and Greece) to rhetoric marking this as a continued hostilities between old foes. Therefore Aeneas and his story merged with the founding story of Rome by Romulus and Remus to create the national narrative of Rome and her people.