Tennyson is famous for making his poems sound like what they're meant to describe, and this poem is no exception. The speaker describes echoes in the mountains, and the poem itself is filled with "echoes" of various kinds. The alliteration, internal rhymes, and the end rhymes echo specific sounds.
Check it out: "The long light shakes across the lakes, / And the wild cataract leaps in glory" (3-4). The alliteration of the repeated L sound and the internal rhyme of "shakes" and "lakes" create little mini-echoes just within that one line. The repetition of the same words ("dying, dying, dying") and the repetition of the same final line to each stanza also help to create echoes. This poem is seriously filled with echoes!
These "echoes" help make the poem sound more like a song than a poem (which makes some sense, given that the poem is about listening to the music of a bugle). Think about how many songs you know that have a repeated refrain or chorus. In fact, this poem has been set to music many times—check the "Best of the Web" section for examples.