Homer defined the idea of the Greek hero in both of his epic poems, the Iliad and the Odyssey. Odysseus definitely fits the mold of a Greek hero.
A Greek hero needed to be strong and brave; willing to die in battle for a just cause; should have above-average intelligence, strength, and beauty; and would have had the gods and goddesses helping him out a great deal, as they wouldn't have bothered with humans who weren't worthy of their help. Odysseus fits the mold perfectly. He is actually known more for his intelligence and craftiness due to his brilliant Trojan Horse idea that made it possible for the Greeks to finally defeat the Trojans. But he needed that same intelligence to finally make it home, having to escape from numerous enemies and creatures that wanted to delay him for a variety of reasons.
In addition to his intelligence, Odysseus proves his bravery time after time in his many battles and fights. He also shows himself to be loyal not just to his men, but also to his family, Penelope and Telemachus. And finally, Odysseus is one of Athena's most favored humans. She goes to great lengths to help him in his quest to return home. Athena would not have wasted her time on someone less than a hero.
If you haven't done so, I recommend that you read the Iliad to get a broader picture of Odysseus. Also check the links below for more information! Good luck!