uncoil
To unwind or straighten something that was curled up.
To uncoil means to unwind or straighten something that has been wrapped in loops or circles. When a garden hose has been coiled up for storage, you uncoil it by pulling it straight so you can use it to water plants. A snake that's been resting in a tight spiral uncoils its body when it starts to move.
Think of a spring: when compressed, it sits in tight coils, but when released, it uncoils and stretches out. A rope stored in neat loops needs to be uncoiled before you can use its full length.
You might uncoil a measuring tape to see how long something is, or watch a cat uncoil from a curled-up sleeping position when it hears the sound of a can opener. The action suggests a smooth unwinding motion, like watching a rolled-up party streamer unfurl. Anything that starts in a coiled, circular, or spiral shape and then straightens out or loosens is uncoiling.