Cats love for boxes may come from a predatory behaviour. Scientists are still not completely certain about the reasons for the affinity cats have for boxes, but the most prominent theory is that boxes offer security and shelter from predators while they stalk prey. Boxes reduce stress levels in cats, and cats that have boxes get used to new surrounding faster than those that don’t. Boxes could also be used to escape unwanted attention, or be used as ideal insulators to keep warm

'Cats like boxes because they are cryptic animals; they like to hide,' Stephen Zawistowski, science adviser for the American Society for the Prevention of Cruelty to Animals 'And a box gives them a place of safety and security.'

http://www.dailymail.co.uk/sciencetech/article-2938758/Why-cats-love-boxes-Scientists-say-predatory-behavior-just-want-leave-alone.html