Ulysses finds his life as a king "idle" because he has the heart of an adventurer and wanderer. He feels trapped and useless at home because what he does—which as king, is maintaining and upholding the law of the land—is not what he was made to do.
Ulysses is not happy or content unless he is out journeying and finding adventure. He contrasts himself to his son, Telemachus, who is content to be at home. Telemachus has a character of "slow prudence" and is "centered" in "common duties." He loves the life of home rule and is contented with it. Because of his skills in this area, Ulysses has faith that his son will gradually "subdue" a wild people and make them useful. As Ulysses says,
He works his work, I mine.
Ulysses defines his "work" in being out at sea: anything else feels idle to him. He understands this is a subjective point of view: it is about who he is, not a judgment on staying home and ruling in a calm, steady way. Because of what surges within him, Ulysses is willing to defy stereotypes about age and is about to set out on another adventure. He knows he may finally die on this journey, but because he has a "heroic" heart, it is what he needs to do.