I believe you are referring to Virgil's famous line in the Aeneid:

[Jupiter said:]...Then Romulus, proud in the tawny hide of the she-wolf, his nurse, shall take up the line, and found the walls of Mars and call the people Romans after his own name. For these I set no bounds in space or time; but have given empire without end.

This was basically pro-Augustan propaganda poetry and specifically called to mind the ages of Man. The Greek poet Hesiod (and others) had the idea of the general decline of man, going through successive stages: Golden, Silver, Bronze, Heroic and Iron.

The best age was the Golden Age, where everyone enjoyed peace and prosperity. Hesiod, in Works and Days, says:

First of all the deathless gods who dwell on Olympus made a golden race of mortal men who lived in the time of Cronos when he was reigning in heaven. And they lived like gods without sorrow of heart, remote and free from toil and grief... they made merry with feasting beyond the reach of all evils... they had all good things; for the fruitful earth unforced bare them fruit abundantly and without stint. They dwelt in ease and peace upon their lands with many good things, rich in flocks and loved by the blessed gods.

Virgil is saying that Augustus is bringing the Golden Age back to Rome. Following the above quote he goes on to talk about the end of war, great prosperity and religious piety - very similar to the idea of the Golden Age in Hesiod. I do not think that educated Romans believed this literally. It was poetry, and almost a panegyric.