A type of long, slender fish (somewhat resembling a snake in appearance). Eel eyes evidently have magical uses. They were sold sold in Diagon Alley (PS5), and standing naked in a barrel of eels’ eyes is part of a remedy for spattergroit, according to one medieval healer (OP23).
An eel farm is owned by Agatha Timms, who bet half its shares with Ludo Bagman that the final of the 1994 Quidditch World Cup would be a week long (GF7).
Eels are not commonly eaten in the U.S. but eel pie, for instance, is eaten in Britain. To take an example from one of JKR's favourite books, when in C.S. Lewis' The Silver Chair, the Marsh-wiggle Puddleglum offered Jill and Eustace eel stew but was dubious about whether humans could eat it or would enjoy it, he was merely giving one of his typical gloomy observations about life, the universe, and everything.