Literature is derived from other literature. This is the case for your Ulysses in Alfred, Lord Tennyson's "Ulysses". This Ulysses is based on the character originally created by Homer in The Illiad and The Odyssey. He was a great greek king who fought heroically and with great military strategy. Known for a close relationship with the gods, we see his character reappear in Dante's Inferno. Although Homer in his tale sends Ulysses home, Dante makes him remain in the Land of the Dead. Dante paints a picture of himself in discussion with Ulysses over the abuse of power.
Finally we learn that Tennyson's Ulysses never took Dante's route, but after he arrived back in Ithaca was bored, unfulfilled and dissatified. Although his wife had waited for him all those years, she is now not as intriguing to him, nor is the power of a throne.
His character is still the heroic leader and cheerleader of his troops, but here we see him long for adventure, even adventure that risks his life.
This is a loaded question. I think that one could write pages or books upon this question. In the Tennyson poem, "Ulysses" refers to the Greek hero who had to battle through adversaries of all types in order to return home to Ithaca after his exploits in the Trojan War. In Tennyson's configuration, Ulysses comes back home, but realizes that he cannot be content with a life of domesticity. After battling monsters at sea, defying the Gods, escaping from sorceresses, and restoring honor to his name and throne, he simply cannot sit at home with Penelope and teach Telemachus how to fish. Rather, he must go back out and "strive, seek, find, and not yield." Within this configuration of the Greek hero, Ulysses represents the irrepressible nature of human freedom that continues to expand and is not at rest with simply being. The vision of humanity given in the poem is one where human freedom is the defining element in the modern setting and the only element that comes to classify who we are and what we do.