The Romans invented myths to explain the foundation of their capital city, Rome. These myths gave Rome a divine origin and linked their history into Greek mythology. These myths were first transmitted orally then from the end of the Republic written down by poets such as Virgil. According to them, Rome was founded in 753 BC.
Originally Rome was a monarchy but in 509 BC a revolt overthrew the last king and Rome became a republic.
Under the Republic, Rome became the capital of a huge empire. When Julius Caesar, victor of the war with the Gauls, was nominated dictator for life in 44BC, a group of senators assassinated him because they feared the return of monarchy. By 27 BC, when Augustus ended the Republic, the Roman Empire extended throughout the whole Mediterranean and the Romans used myths to justify their rule.
Watch first 1m30 for a little introduction to the myth of Romulus and Remus: