[The Ashwinder] is born from the embers of untended magical fires, and so is particularly dangerous to wizards who are not mindful of their fires when cooking or brewing potions ... The Ashwinder’s glowing red eyes are a useful way of spotting it hiding in the dark corners it prefers.
-- notes written by Zygmunt Budge in The Book of Potions (BoP)
The Ashwinder is a thin grey serpent with glowing red eyes which comes out of untended magical fires and lives long enough to lay fiery hot eggs in some dark and secluded spot. These eggs, while valued as potion ingredients, are very dangerous. If they are not found and frozen in time, they will set buildings on fire. They are found all over the world (FB, BoP).
Care of Magical Creatures professor Silvanus Kettleburn performed an engorgement charm on an ashwinder he provided for the role of the giant worm when Herbology professor Herbert Beery put on a pantomime of Beedle the Bard's tale "The Fountain of Fair Fortune" as part of Hogwarts' Christmas celebration. It didn't go well (TBB/FFF, Pm).
"Ash" comes from the color of the serpent and also as a reference to its connection to fire. "Winder" recalls the sideways movement of some kinds of snakes, such as the rattler. They are sometimes called "sidewinders."
It's possible that this creature was inspired by a firework called "Black Snake", which creates a snake-like trail of ash behind it as it burns. (source: Wikipedia) -BB