In what ways did Odysseus demonstrate heroic behavior?
Odysseus demonstrates heroic behavior when he and his crew stop in the Land of the Lotus Eaters. Wary, he sends only three men to scout the island and find out who lives there and what the inhabitants are like. When these three men eat the lotus flower, they no longer want to go home. Rather than leaving them there, he personally retrieves them and physically wrestles them back to the ship. His actions, here, are heroic because he looks out for his men's welfare when they are incapable of doing so themselves.
Odysseus also shows his heroism when his quick thinking and bravery allow him to come up with a plan to wound Polyphemus, the Cyclops, so that he cannot catch Odysseus and his men. He realizes that he cannot kill the monster or they will not be able to move the stone in front of the door (and so they would all die). Instead, he comes up with a plan to blind Polyphemus so that he will still be capable of removing the stone, but he will not be able to see the crew to catch them. Odysseus is one of the handful of men to climb atop the monster while he is sleeping and plunge the olive stake into its eye. This bravery and cleverness are both heroic.
Finally, Odysseus's loyalty and devotion to his wife and son are likewise heroic. He could have stayed with Circe or Calypso, both beautiful goddesses who would have kept him forever. He could have simply given up after years and years of struggling to get home, setbacks from his crew, and so on. But he doesn't. He keeps fighting to get home to the family he loves no matter what. This loyalty to his wife, Penelope, and his devotion to his family and home are quite heroic as well.