what do you mean by "The glory that was Greece, and grandeur that was Rome"?

Answer 1

Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, which begins roughly with the earliest-recorded Greek poetry of Homer (7th century BCE), and continues through the rise of Christianity and the fall of the Western Roman Empire (5th century CE), ending in the dissolution of classical culture with the close of Late Antiquity.

Such a wide sampling of history and territory covers many rather disparate cultures and periods. "Classical antiquity" typically refers to an idealized vision of later people, of what was, in Edgar Allan Poe's words, "the glory that was Greece, the grandeur that was Rome!"

Thus Poe is talking about modern day people's conception of what those civilisations were actually like. Greece had a glorious period when it conquered many adjoining countries led by such as Alexander the Great and depicted by Homer. Rome's grandeur was displayed in the many treasures and riches brought back by it's armies who conquered most of Europe including parts of Asia and Africa.

Answer 2

This should help explain it: http://en.wikipedia.org/wiki/Classical_antiquity