Mine do that, too. My guess is that there's something yummy smelling around the nail bed. I don't mind the fingernail gnawing so much, but I cover the couch with a drop cloth and use it for their out of cage time (they seem to like it better than the bathroom floor or the card table, and no other places are rat-proofed yet). Davey has decided he loves to nibble my toes when I'm not wearing socks or anything. That can get painful pretty quickly on that sensitive skin! I'm really hoping if I keep eeping and moving my feet away, he'll get the picture.
Both my ratties chomp down on my fingernails. They don't really chew, but seem to be trying to bite through them. They don't go down as far as the skin. I kind of like how it feels, and sometimes do a little tug-of-war with them. Once, Beauregard gave me a little pedicure (or at least tried). It was hilarious! I think biting is one way rats explore something they can't figure out. They often bite into and tug my sleeve if my arm is blocking their way out of the cage, and they will occasionally just spontaneously bite my clothing--a little dreg of food or drink there? Who knows! They love to shred paper and cloth, so I have to be very careful what kind of cloth is around them when they are out.