The speaker says he can read the "body's discourse" in every creature, meaning he understands what animals express through posture, movement and sound. That sounds like a gift, but the poem quickly shows its cost. He admits that a wise man wouldn't bark or caw without good reason, as if answering animals is a bit foolish, or at least something to do sparingly. Yet when he hears the "melancholy call of a swan," he answers anyway.
The last two lines turn inward. The swan's sadness doesn't stay outside him; it becomes "the void turning into despair / in my stomach." Understanding another creature's grief means feeling it physically, and the emptiness he senses shifts from something heard to something felt. The mood is quiet, lonely and a little eerie. The short, plain lines leave a lot of space around them, which makes the speaker's closeness to the swan feel both tender and heavy.