Odysseus is not just a hero in the traditional sense—a brave, noble warrior who acquits himself with great courage on the battlefield. He's also a thinker: not an intellectual, to be sure, but someone who thinks carefully about his next move. A great example of his thoughtfulness comes when he assists Diomedes in the skillful night operation to kill Rhesus's horses. It had been foretold that if these horses drank from the Scamander river, then Troy would not fall. Odysseus pays careful attention to prophecies and divine omens, and this helps stand the Achaeans in good stead in their long, drawn-out battle with the Trojans.
In this case, as in so many others, Odysseus displays heroic behavior in that he's thinking about what's best for the Achaeans as a whole, not just for himself (unlike Achilles, for example). Odysseus does an incredible job throughout The Iliad restoring order and morale to the Achaean camp, in the midst of all the petty squabbles and clashes of ego. This, more than any of his numerous acts of physical bravery on the field of battle, is what makes Odysseus a new kind of hero.