Corpses are the bodies of your slain foes. Most corpses are made of flesh based on the monster slain, except for several monsters with special body material such as imps, whose bodies are made of sulphur.
Corpses will eventually rot away, but before that, feel free to eat them to ease you hunger. Note that corpses are best eaten fresh, as spoiled corpses will confuse you and may cause you to become parasitized. While most corpses are edible, some are not and some may even have detrimental effects on your character: see here for further information.