Whenever I bring a box home, or I get a package in the mail, both of my cats immediately have to inspect it thoroughly. As soon as it's empty, they'll be playing games with it: jumping in and out, guarding it from the other, etc. If I toss a toy into a box, they'll drop whatever they're doing to immediately get the toy. I've noticed that they'll even grab one of their toys to bring it into the box to play with.
Why do cats love sleeping on cardboard? doesn't explain why cats play with cardboard as mine do. My cats sleep on the bed with me; they don't sleep in the boxes except for a few occasions where they wear themselves out and don't feel like leaving the box to sleep.
Their playing reminds me of kids playing with their imaginations, turning boxes into spaceships and things like that. What is it about boxes that cats enjoy?