Eurylochus is a minor character in Homer's The Odyssey. He is a captain in Odysseus' army. His main function is to serve as a foil character to Odysseus. The reader sees Eurylochus' cowardice and contrasts it to Odysseus' undaunted courage.
Probably the best example of Eurylochus' cowardice is when the army lands on Circe's island. The men see her palace off in the distance, and they are worried that the inhabitants will attack them. Eurylochus leads half of the men to investigate the palace, while Odysseus waits with the other half. However, Eurylochus "suspected a trap and stayed outside," (The Odyssesy Book 10 line 232) leaving his men to investigate by themselves. After Circe transforms his men into pigs, it is ultimately Odysseus who has to go save them with the help of Hermes.