Image Scott Branson, Flickr
Have you ever noticed that you empty out the contents of a box, turn around and find the cat has jumped in there? There are lots of theories around why cats love boxes, we will never know for sure as they aren't going to tell us, but there are several logical sounding theories as to why this is.
They like to hide:
Image Moe Alves, Flickr
In the wild, cats have larger predators such as foxes. Therefore, it is in their best interests to be as inconspicuous as possible, especially when they are at their most vulnerable, while they sleep. Finding a quiet "den" makes sense. If he's hidden away, predators are less likely to find him.
Not only does a box provide a hiding spot that your cat will go for, but an enclosed "cave" would have provided a cat with protection from the elements. Cats will instinctively seek out somewhere snug and sheltered.
Image Michael Franz Franz, Flickr
Cats are nosey, they like to investigate almost anything new that comes into the house. They will circle it, slowly getting closer and closer until they can tentatively sniff it, if all is well, they will jump on it or in it. That goes for boxes too. If they're lucky, they might find something interesting IN the box to play with. A piece of packaging that they can bat around like a mouse.
The curiosity angle holds true with me because it's not just boxes that cats seem to have a fascination with. Every cat owner will tell you that your cat will hop into a suitcase the second you bring it out to pack your clothes into. We also have two cats who will jump into a cupboard the moment the door is open. Cats just like to check stuff out.
They like to stalk:
Image Nicola Romagna, Flickr
When a cat stalks he will get down low and ambush his prey. A box makes a perfect stalking spot. Have you ever walked past a box and been pounced on by your cat?
Texture and sound:
Image evan p cordes, Flickr
The sound of paws and claws on a box is cool to a cat. It makes a lot of noise, it feels good. Cats like to chew the corner of boxes. I assume they must like the texture on their teeth and gums.
Cardboard also provides your cat with the opportunity to scratch, sharpening his claws and marking his territory.