Well the names pretty much tells you the answer but if you want a detailed answer then here it is: The Dionysian festival honored the Greek god Dionysus, who was the Greek god of wine. During this festival the Greeks would harvest their grapes, because this was the time when they were ripe, and would have a big feast while drinking the wine that they had made. But not until they had given a burnt portion of it to Dionysus.
