"The Owl and the Pussy-cat went to sea / In a beautiful pea-green boat"
The opening lines of the poem establish the foundation of the plot. An owl and a cat have set sail in a boat. Supplies include honey as might be expected, but also paper currency would not be expected. The narrator is merely a storyteller and not a participant. The most significant aspect of these opening lines is that the animals have clearly been anthropomorphized, but within a world in which such personification is not unusual or unexpected. That a cat would fall in with an owl rather than seeing it as prey is a given that is not to be questioned.
"O let us be married! too long we have tarried: / But what shall we do for a ring?”
After having a love song sung to her by the bird, the cat compliments the Owl's elegance and voice. Then she cries out for them to be married, finally, after having waited far too long. The next lines, spoken by the narrator, inform the reader that this little boat voyage will last for 366 days. Pussy-Cat's yearning to be married after waiting so long is complicated by the lack of a wedding band. This becomes the centerpiece of the plot for the rest of the story. It also cements the personification of the animals within a world recognizably inhabited by humans.
"So they took it away, and were married next day / By the Turkey who lives on the hill."
The issue of the lack of a ring signifying marital union is resolved when the pair make landfall in a strange place far away. The Owl and Pussy-Cat find a Pig who sports a ring through his nose and offer the swine a shilling as fair recompense in exchange for the ring. Also in this strange land is a turkey taking up residence at the top of a hill. Interestingly, the Turkey's actual legal ability to perform a marriage ceremony is neither addressed nor explained. In the universe in which this story takes place, it just seems to be a given that turkeys are animals upon which have been conferred the right to carry out this ritualistic responsibility. After the ceremony, the Owl and the Pussy-Cat return to the beachfront on which they made landfill and dance the night away, illuminated only by the shimmering moonlight. The poem thus ends up exactly where it began. Readers are encouraged to simply accept that things are the way they are and to avoid scrutinizing the details too closely.