Ever have something when you were a little kid that you were kind of weirdly attached to, like a blanket, a teddy bear, or something else? Well this poor little kid had books and his kitten, Fluffy. With no friends to speak of, this kitten became his one and only. Check it out:
My aunt died soon after of pneumonia, in the hospital. That evening my father arrived home from work and he brought a cardboard box with him. In the cardboard box was a soft-haired black kitten of uncertain gender, whom I immediately named Fluffy, and which I loved utterly and wholeheartedly. Fluffy slept on my bed at night. I talked to it, sometimes, when my little sister was not around, half-expecting it to answer in a human tongue. It never did. I did not mind. The kitten was affectionate and interested and a good companion for someone whose seventh birthday party had consisted of a table with iced biscuits and a blancmange and cake and fifteen empty folding chairs. (1.7)
Aside from how sad this image is (and how the boy is well on the path to becoming a crazy cat dude in his old age) the kitten is more than just something to talk to—it is a symbol of his childish innocence, and the blissful ignorance that goes along with it.
When the opal miner shows up at his house though, Fluffy meets an untimely demise and is hastily replaced by an angry old tomcat. The kitten, the symbol of his childish innocence, is killed off at exactly the moment the boy embarks upon an adventure that will similarly rob him of his ability to believe in a world that is much simpler than the one the Hempstocks inhabit.
So instead of his sweet, purring fluffball that sleeps on his pillow, the boy is confronted with reality: that life is sometimes a snarling, mangy mess that you feed every once in a while to keep it around.
Similarly, right after their first encounter with the angry circus tent that is Ursula Monkton, Lettie lets him pull a kitten right up from the ground in a field of cattails. It's a lot like Fluffy, and he wants to bring it home with him (us too), but Lettie doesn't think it's wise to bring something home from "these parts."
And yet, the kitten keeps reappearing just when the little boy needs her. The night he sleeps at the Hempstock's farm she curls up right on his pillow to comfort him as he slumbers. Then, when all of the events are over and he thinks Lettie has just gone off to Australia, the kitten miraculously shows up at his back door:
My parents, who had never noticed the ginger tom's disappearance, did not initially notice the arrival of the new kitten-cat, and by the time my father commented on her existence she had been living with us for several weeks, exploring the garden until I came home from school, then staying near me while I read or played. At night she would wait beneath the bed until the lights were turned out, then she would accommodate herself on the pillow beside me, grooming my hair, and purring, so quietly as to never disturb my sister. I would fall asleep with my face pressed into her fur, while her deep electrical purr vibrated softly against my cheek. She had such unusual eyes. They made me think of the seaside, and so I called her Ocean, and could not have told you why. (15.49)
First of all, what kinds of parents are so oblivious that they don't notice a new pet when one shows up? If a strange cat showed up in the house most parents would at least be like this. But space cadet parents are the least of this kid's problems—while the kitten still symbolizes innocence and companionship, this particular kitten might just be a piece of Lettie that's keeping an eye out for him.
As he's sitting by the pond at the end of the book, he remembers that Ocean had grown into a cat, and that he'd adored her for years, but he can't remember what eventually happened to her. In a morbid moment he thinks: "It doesn't matter that I can't remember the details any longer: death happened to her. Death happens to all of us" (Epilogue.2). For a fun experiment, try replacing "her" and "us" with the word innocence. Spooky.