in ancient Japan, they are considered lesser oni, evil kami or malicious yokai - which puts them in the category of beings like the Norse Trolls or Fairies as a generic name for a wide variety of related monsters and spirits (also much like the modern use of "demon").
The most well-known tale about amanojaku is the story of Uriko hime. In this story, a childless elderly couple discovered a baby girl inside of a melon. They took her home and raised her as their own, and named her Uriko hime. She grew into a beautiful young woman, and one day a request for her hand in marriage arrived. Delighted, her parents went off to town to purchase her dowry and prepare for her wedding. Before leaving, they warned her not to open the door for anybody, no matter what!
Shortly afterward, Uriko hime heard a knock at the door. “Uriko hime, please let me in!” She refused to open the door. The voice replied, “If you won’t open the door, then at least open the window a crack…”
Reluctantly, Uriko hime opened the window just a crack. As soon as she had done so, a long, clawed finger slipped into the crack and smashed the window open. It was an amanojaku! The amanojaku leaped at Uriko hime, tearing at her clothes. The young woman fought for her life, biting and kicking at the demon, but she was not strong enough. The amanojaku snapped her neck, and she died.
The amanojaku didn’t stop there, however. It flayed Uriko hime’s skin and wore it like a suit, hiding in her clothes and disguising itself as the young girl. When the girl’s parents came home, they were fooled into thinking their daughter was still alive.
Finally, the wedding day arrived. The elderly couple brought the amanojaku-in-disguise to its husband-to-be. However, a crow in a nearby tree called out, warning the couple that their daughter was not what she seemed. They grabbed the bride tight and held her down. They washed her body until the flayed skin sloughed off, and the amanojaku was revealed.
The amanojaku ran for its life, but the elderly couple chased after it. More and more people joined them until a whole host of villagers chased the demon through the village. Finally, the townspeople caught up to the amanojaku and hit it with sticks, stones, and tools. They beat the demon into a bloody mess, and it died.