This article is from the Hellraiser movie FAQ, by Mario Moeller and Kalle Paulsson karl-pau@dsv.su.se with numerous contributions by others.
"The box. I don't know where it came from. I don't know who made it
or why. I only know what it does. It hurts. It hurts. I don't
know. It kind of opens itself. Your fingers move. You learn. It
wants to open, that's the thing. And it knows when you want to open it.
And it helps. And it opens. And then they come. The Cenobites.
The demons. You might think it's delusion, but it's not. I saw them.
I looked into their eyes and they looked back at me. Creatures
from Hell."
The puzzle box featured in the Hellraiser films is called Lemarchand's box,
constructed by a master craftsman. The movies refer to it as the Lament
Configuration, which is a way to raise hell. Literally. The riddle
associated with the box is that if you solve the seemingly impossible
puzzle, your any whim and pleasure will be met. You will be taken to the
boundaries of your pleasure, and beyond.
But if subjected to too much of a certain pleasure, it isn't a pleasure
anymore. In the original novella, Frank, upon solving the box, is given
his every sexual pleasure except that every bodily sense of his becomes
affected - and it doesn't stop there. His sensations became higher still,
until it became painful, and he begged to stop. Hell is what he wanted,
and hell is what he got.
(from the novella):
"As it was, they had brought incalculable suffering. They had overdosed
him on sensuality, until his mind teetred on madness, then they'd
initiated him into experiences that his nerves still convulsed to recall.
They called it pleasure; and perhaps they'd meant it. Perhaps not.
It was impossible to know with these minds; they were so hopelessly,
flawlessly ambiguous. They recognised no principles of reward and
punishment by which he could hope to win some respite from their tortures,
nor were they touched by any appeal for mercy. He'd tried that, over the
weeks and months that separated the solving of the box from today."
 
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