To uncoil is to straighten something out that's been curled or twisted, the way you uncoil a long, thin piece of red licorice, chewing it as you go.
When something is coiled, it's wound or curled into a spiral shape. You can even call it a coil, like a coil of rope on the deck of a sailboat. Make it straight by untwisting it, and you uncoil it: "Leave my snake alone! Don't try to uncoil her!" The prefix un- means "reverse or opposite of," and coil, "gather into rings," comes from a root meaning "to gather or collect."