What do you call those strips on the side of your fingernail that hurt or bleed !

I, and most people I know have these little white lines on the edge of my fingernail that stick out and rub against things, which is very irritating but not painful. When I try to pull them out sometimes my finger bleeds in the corner where its "root" was, so to speak. Whether it bleeds or not, if I try to pull it out it always leaves my finger slightly puffy and sore around the area. They seem to be made out of something that is in between keratin and actual skin; I cant quite figure out what it is. In any case I'd like to stop seeing them. Also what are they called?