A frame story is a story in which several other stories are written within. In this case, the entirety of Shahrazad's storytelling to the evil king occurs within the frame story of the king's anger at all women. This story also influences Shahrazad's storytelling, since she must tell an interesting enough tale to keep the king intrigued and make him not want to her and many other women after her.
The story of Scheherazade and the evil king is a frame story because it is a basis and a solid basic structure on which bigger things can be built for all the other stories. It is a literary technique that serves as a companion piece to the story within a story. The Arabian Nights is a collection of stories by Islamic authors. Though each collection features different stories, they are all centered around the frame story of Shahrayar, Shahzaman, and Scheherazade. Scheherazade is the primary storyteller of The Arabian Nights.
