Tennyson's well known short work is based upon the Inferno by Dante. It was very remarkable to hear it read out loud in part by Bruce Boxleitner in the Babylon 5 episode The Long Night. Upon his return home from the Trojan War Ulysses became restless and set about on new voyages. Tennyson's friend Arthur Hallam had just passed away when he wrote this poem and he was looking for some kind of closure, a way to move forward in his own life and to come to an understanding about his own mortality.
The line where Ulysses explains that his son, Telemachus, will "pay meet adoration to my household gods" when Ulysses departs seemed like an admonishment to me. I thought the teacher was up to some kind of trick when she assigned us to study this poem in English class and I moved away before I could really get a handle on it so it was a mystery to me. Years later now as a parent whose job is dissipating as my sons become more and more responsible, the meaning is as straightforward as it appears and really a coming of age tale. One of saying goodbye to times and friends who have passed on, finding his place in the world, and Ulysses encourages (rather than what I thought was an admonishment as a teen) as a parent, for his child to carry on and do a good job.
I have since discovered that the old Romans celebrated the Feast of Mars on March 6th honoring the household gods, Penates and Lares, who were figures of importance in the Roman ways of their religious life. Since every householder was a priest this is simply what Ulysses is telling his son that he will take over as head of the household and oversee his duties while he travels onward. Hallam is Ulysses gone off to face unknown and new horizons leaving his legacy behind for Tennyson where He works his work, I mine.