What does Odysseus' bow represnt in The Odyssey?
That is a great question. I think we can look at it in several ways, but here is one approach. For one thing, the very fact that Odysseus is the only one that can use the bow in book twenty-one shows that he is physically strong. However, Odysseus is not known for his strength, but his cunning. This is how is defeated Polyphemus and the suitors. So, it seems that the point of the bow is a reminder that while he is a powerful warrior, but what is even more important is person's cunning. This is certainly how Odysseus is portrayed in later literature.
Odysseus’ bow was a gift that only he would be able to bend and string for shooting. It symbolizes Odysseus’ right to be kind of Ithaca by using it to reclaim his kingdom by defeating the suitors with it. Penelope has promised to marry the suitor that could bend and string the bow and then shoot an arrow through the axe-holes. Ulysses was the only one who could, and he then turned on the suitors, killing them. The bow also represents a link between Odysseus and heroes of the Greek myths.