This particular quote is steeped in the Romantic notion of nostalgia for the past. Being a Romantic thinker himself, Goethe believed that the Greeks "got it right" and in examining their past, there might be a chance for replication in the present. In their pursuit of "the good, the true, and the beautiful," thinkers like Goethe felt that there was a redemptive spirit to individual pursuits. This would have been enhanced through Socratic/ Platonic philosophy, which stresses that there is a transcendental notion of the good to which humans must strive. This is concurrent with the Romantic philosophy that stresses the pursuit of an artistic, social, and personal notion of the good which can only be appreciated by the few. The idea of Greek "arete" in battle and in endeavors- where greatness is highly evident for all to see- is something that Romantic thinkers admired. Individuals like Lord Bryon saw themselves as "warriors of the truth" and did everything in their power to replicate this Greek notion of honor and greatness on the battlefield. At the same time, the spirit of the polis- of democracy in action- where all individuals discuss and reason out problems appealed to the Romantic thinkers for it was in stark contrast to government being a vehicle for the needs of the few. In the mind of Goethe and the Romantics, the Greeks envisioned and dreamt of life in the best manner possible, proving that their notions of transcendence "got it right."
Arete means excellence in Greek. The idea behind this is that the Greeks excelled in many areas. And, indeed, if one studies the Greek in any detail, one will immediately realize that the Greeks did excel in a lot. For example, there were great strides in science, philosophy, medicine, and the arts through the Greeks. Consider some of the names that are associated with the Greeks - Hippocrates, Socrates, Sophocles, Aristotle, and Demosthenes. Even today we read and contemplate what these men have written! There influence is felt now. Also when we look at Athenian democracy, we will be even more impressed, because their form of government is the basis of ours in America.