"The Tide Rises, the Tide Falls" is a poem about cycles. While you might think just based on the title that's a poem about the motions of the tides, it's about more than that. It's about the circle of life itself. In this poem, the tides are just a metaphor for the ups and downs of life, the natural cycles of life and death.
The title itself is really neat in that it very cleverly communicates the poem's interest in cycles. For example, did you notice how the first two words in each part are the same ("the tide")? Did you notice how the long I sound is repeated in both "tide" and "rises"? Did you notice how the final word in each part of the title ends in S? (Check out "Sound Check" for more on this.) All this repetition in the title is deliberate. You could say that the title itself is a miniature cycle: things start out in one place, and they end up in pretty much the same place, with a few small differences. That's exactly what the speaker says in the poem.
The traveler described in the second and third stanzas eventually dies, but life continues on—there's a hostler, there's some horses ripping and roaring and ready to go, and the tides continue in their eternal rise and fall. The traveler is gone, never to return, yes, but the world and its cycles keep going, substantially the same (but minus, of course, the traveler).