Grab your time machines because we're headed way back. Running from roughly 1200 BCE to 455 CE, the classical period was home to the great works of ancient Greece and Rome. You'll sometimes see the words Greco-Roman or antiquity used to refer to this millennia-old period.
The classical period was a golden age for literature and the arts, take it from Shmoop. The big writers from this period include all those Greek and Roman guys who wrote epics, like Homer of the Iliad and Odyssey fame, and the Roman poet Virgil who wrote the Aeneid. The Greek philosophers Plato, Socrates, and Aristotle called this period home, as did Greek dramatists like Euripides and Aristophanes. As for poets, Horace and Ovid were two of the most influential.
What did these writers have in common? Well, when people talk about classicism they talk about literature that is distinctive for its balance, order, and reasonableness. Aristotle's Poetics was super important in defining these features for drama in the following centuries, as was Horace's Ars Poetica. For Horace, poetry was supposed to be "dulce et utile," or "sweet and useful."
So fab was the classical period that later writers, beginning with the Renaissance, often imitated the style of classical authors. This tradition of imitation is where we get the term neoclassical, or new classics.
For more on the classical period, be sure to check out Shmoop Mythology.