3 layers of skin, the nerves being in the 2nd and 3rd layers..........the papercut only passes through the first and perhaps 2nd layer, leaving the nerves intact but completely exposed..............like the nerve of a tooth.
It is this exposure that makes papercuts so painful.
I'd heard somewhere that it is because tiny bits of paper get left in the cut so (unhygienic as it may be) if you suck the cut it gets the paper out and makes it better.