Why cats love boxes. They just really love the hell out of boxes. Have you ever noticed this? I'm certainly not complaining. I adore cats, especially cats in boxes. I don't, however, understand their ardent appreciation of cardboard.
My hypothesis is that it helps them feel safe. It gives them a place to hide, a place to be warm... It's all about security, I think. And I guess it gives them a space demarcated as their own. (Those claw markings clearly indicate the owner of the box.)
More than that: it's also a look-out. From their box-vantage, they can see and hear all that occurs within their purveyance while staying "enclosed" or "hidden" in their cardboard shelter. I use quotations because often times the box is not closed. In fact, my cat Gwenevere has lately found sanctuary within a box that is actually completely open (see pictures).
I also don't get why cats love sitting on paper.... Any of you ever thought about these things? These are important questions! The questions of our time!
I will leave you with some video of an awesome cat named Maru. The first one demonstrates his love of boxes; the second one gives you an introduction to his whole world (it's a little longer).