Three short lines tell a very small story: a person and an aging dog walk out to see a seal, then walk back without speaking. Nothing dramatic happens, and that is the point. The poem trusts a simple outing to carry its feeling.
The most telling detail is the last line. "No words all our way home" could mean the speaker and dog are simply comfortable together, the way close companions often are. The word "old" nudges it toward something more tender, though. Judging by that choice, the speaker may be aware that these walks are numbered, and the silence could be a kind of attention, or a quiet awe at what they've just seen.
The mood is calm, gentle, and a little wistful. The title, "Harbor," suggests a sheltered place, and the poem itself feels like one: a small, protected stretch of time where company is enough and nothing needs to be said.