Source : Webster's Revised Unabridged Dictionary (1913)

Hangnail \Hang"nail`\, n. [A corruption of agnail.]
   A small piece or silver of skin which hangs loose, near the
   root of finger nail. --Holloway.

Source : WordNet®

hangnail
     n : a loose narrow strip of skin near the base of a fingernail;
         tearing it produces a painful sore that is easily
         infected [syn: {agnail}]