And snowy summits old in story (2)
The "old stor[ies]" alluded to here suggest a kind of literary "immortality" that the poet himself perhaps aspired to.
O love, they die in yon rich sky, They faint on hill or field or river: (13-14)
We can't help but wonder, though, if these echoes—which, though they repeat, eventually do "die"—suggest that we may live on in the memories of our loved ones, but only for a time. (After all, they'll die too, right?) Eventually, like the echoes, we will also fade away.
Our echoes roll from soul to soul, And grow for ever and for ever. (15-16)
The speaker is no longer just thinking about literal echoes from the bugle blast—now he's thinking about the kind of echoes that we leave behind us when we die. These figurative "echoes" touch other people. They "roll from soul to soul," and just keep expanding instead of dying out and fading away like a literal echo. Is the speaker suggesting that our impact, or our "echo," will live on forever?