The period you are asking about is known as the golden age of Ancient Greece because it was a period in which Greek civilization achieved many important things. Much of this achievement is associated with the Athenians.
This golden age in Greece was a period when the Greek world experienced a great deal of cultural growth. This was the time when Herodotus and Thucydides essentially invented the modern practice of writing history. It was a time when theater was flowering with playwrights such as Aeschylus, Sophocles, and Aristophanes. The golden age also saw other kinds of achievements. It was a time when philosophers such as Socrates and Plato were alive. It was a time when Greeks were able to achieve such architectural marvels as the Parthenon. It was also a time when Greek sculpture was becoming more lifelike and beautiful. Perhaps of greatest importance to us today, however, is the fact that this was the time in which Athenian democracy was at its peak.
For all of these reasons, this time period in Ancient Greece is seen as a golden age.