Odysseus as a character personifies what was valued in the ancient male in Greek culture. First, he is very, very strong and a brave warrior, which are the highest attributes a man can possess in his society. He fought bravely and with honor in the Trojan War, and is a courageous and respected leader of his men as they journey homeward.
Odysseus is also a wily and resourceful thinker, a trickster who is good at using his wits to outsmart enemies who are stronger than he is. For example, although he is physically weaker than the barbarous Polyphemous, Odysseus outsmarts him and attacks him at his most vulnerable point by taking out his single eye. This allows Odysseus and his remaining men to escape Polyphemous before ending up on his dinner plate. This kind of trickster "street smarts" was highly valued by the Greeks: for example, tricking their enemy with a "gift" was how they won the Trojan War.
Loyalty to wife and family was also an important value in Greek society, and Odysseus wants badly, at least after awhile, to get home to his beloved Penelope and his kingdom.
The epic poem also, however, reflects a double standard in Greek culture. Because Odysseus is a man, he is able to linger with more than one alluring female lover, delaying his trip home. Penelope, in contrast, has to stay pure and can't possibly risk her reputation dallying with a man while awaiting her husband's return. To be a worthy wife to Odysseus, she must stay chaste.
The poem also reflects the Greek belief that the gods are near and directly intervene in human affairs. It can be startling to modern readers the way Athena so often seems to be hovering in a corner of the same room as Odysseus, or is in some other way near at hand.
Odysseus is product of his time in his strength, courage, wit, and desire to be home with his wife, as well as for his infidelities. The poem also reflects the beliefs of its time in depicting the direct intervention of gods and goddesses, such as Neptune and Athena, into human lives.