When we speak of Odysseus, we are speaking of one of the original heroes of the ancient world. He is probably the best known hero apart from Achilles and Hector. From this perspective, we can say that there were two archetypal heroes in the Greek world. The first one was Achilles. This is the type of hero that we automatically think about. Achilles is a fierce warrior who knows no fear. He lives for glory. For example, when he was given the option to live a long life or die a glorious death as a young man, he chose the second option. To Troy he went and made a name for himself.
The second type of hero is Odysseus. He is very different than Achilles. What characterizes Odysseus is not so much military prowess but cunning and craft. He is the one who knows how to talk to people, smooth things over when there is conflict, the one who through strategy can win battles. According to the Homeric tradition, it is Odysseus who builds the wooden horse to defeat the Trojans. In addition, he is the one in the Odyssey, who outwits the Sirens, Circe, and Polyphemus (to name a few).
In summary, Odysseus is the warrior of craft and Achilles is the warrior of brawn.
But what is his relation to the women of the story? How does it relate to him being a hero?