Someone has apologized, and the speaker can't stop hearing it. The word sits in their head "like chains," which suggests it weighs on them even as it heals. The speaker admits they never expected this kind of sincerity, a person willing to set aside their own pride, or perhaps their old self, out of fear of losing "our last strand" of connection.
What follows is a sense of renewal. Things are back to normal, but deeper, with more to say and feel. The line "You do exist. I do exist" reads like a quiet astonishment that both people are really present to each other again.
The short lines that follow, where everything seems pretty and calm, carry a soft, almost dreamlike glow. Then the ending turns it over: being this happy makes the speaker afraid to die. The mood is tender and grateful, but with a nervous edge, as if the speaker has suddenly found something they could lose.