A chicken meets a stranded whale on the beach, and the encounter turns absurd fast. The chicken confides in him about epilepsy and chronic headaches, the whale seems not to listen, and then he turns green and throws up all over her. The title hints at what that mess might be: ambergris, a substance whales produce that is prized in perfume. The poem never says so outright, so that's an inference, but it fits the "strange, sweet perfume" at the end.
The speaker's tone is deadpan and oddly accepting. She isn't disgusted. Swallowing some of the stuff seems to keep her healthy for weeks, so the whale's unwanted response becomes a kind of accidental cure. The poem suggests that being heard isn't the only way to be helped. By the end, the mood has softened into gentle nostalgia. She goes back to the beach, and the memory drifts in on the breeze, as odd and pleasant as the meeting itself.