what does the period refer to?
It covers the period of Mediterranean history between 323 BC and 30 BC.
Hellenistic period
The Hellenistic period covers the period of Mediterranean history between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in 31 BC and the conquest of Ptolemaic Egypt the following year. 
who was philitas of cos? He was a scholar and poet during the early Hellenistic period of ancient Greece
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Hellenistic period [SEP] Introduction
The Hellenistic period was characterized by a new wave of Greek colonization which established Greek cities and kingdoms in Asia and Africa. This resulted in the export of Greek culture and language to these new realms, spanning as far as modern-day India. Equally, however, these new kingdoms were influenced by the indigenous cultures, adopting local practices where beneficial, necessary, or convenient. Hellenistic culture thus represents a fusion of the ancient Greek world with that of Western Asian, Northeastern African and Southwestern Asian. This mixture gave rise to a common Attic-based Greek dialect, known as Koine Greek, which became the "lingua franca" through the Hellenistic world.