An eel is a fish that's so long and skinny it resembles a snake. Most eels live in very shallow ocean waters, burrowing into the sand there.
Eels are a type of fish, and though they are as long and flexible as snakes, they don't have scales, and if you look closely you can see they have a long, low fin. Eels are famous for being slippery, and in fact to be "as slippery as an eel" means to be so sneaky and cunning that you can get away with something illegal or illicit. This figurative meaning dates from the 16th century.