In the section ,Circe, Odysseus is telling the story about Eurylochus and his men's encounter with the Enchantress Circe. His men landed ashore the island and began to explore. They came across a cave with an elderly woman in it. They heard her singing and Polites reassured them that she wasn't dangerous and walked in. As she prepared a meal of cheese and barley and honey with wine, she added her own vile pinch to make them lose their thought of their fatherland. She flew behind them and turned them into pigs and tossed acorns to feed them. Only Eurylochus escaped to let Odysseus know that Circe had turned them into pigs by saying... "our friends were gone..."
This scene is important because it leads Odysseus into the land of the dead which is another scene in part one.
It is also important because it is a lesson to all Greeks that they are required to show hospitality as Circe did not.