Other forms: unspooled; unspooling; unspools
To unspool is to unwind something that's coiled around a cylinder. If your cat unspools your thread, it'll be impossible to get it all untangled and wound back up.
Anything that's wound around into a spool or coil, can be unspooled. You might unspool the garden hose to fill up a backyard kiddie pool, or unspool the enormous amount of spaghetti from your fork and start over. Figuratively, something that's gracefully or smoothly rolled out is also unspooled: "Grandma loves to unspool a real nail-biter of a story after dinner."