A speaker rises early and walks up and down a ship, and that small routine is nearly all the poem gives us. The title, "Steerage," points to the cheapest part of a vessel, yet the walking is described in surprisingly rich terms: "the most epicure-like going." An epicure is someone who takes refined pleasure in food and drink, so the speaker seems to treat a simple stroll as something to be tasted and enjoyed.
That contrast is what makes the poem interesting. The setting suggests modest means, but the attitude is one of luxury. The phrase "nothing but" implies the speaker has little else, perhaps no destination to think about yet, only the motion itself. Judging by the wording, the feeling is quiet contentment, even delight.
The mood is calm, attentive, and a little playful. Short lines and the repeated sense of "up and down" mimic the steady rhythm of pacing, so the reader walks along with the speaker.