Scheherazade defers her execution by ending each night's tale at an unresolved moment, so the listener's desire to know the ending overrides his intent to kill. Suspense converts the audience's own curiosity into a mechanism that keeps the storyteller alive.
A single outer narrative (Scheherazade and the king) contains many embedded stories, and characters inside those stories often tell further stories of their own. The frame organizes unrelated material into one structure and lets each inner tale comment on the situation of its teller.
The king, embittered into killing each bride after one night, is gradually changed over the nights by exposure to stories about justice, mercy, and consequence. The book presents repeated narrative, not argument or force, as what eventually dissolves his resolve to kill.