To curl oneself or something into a small, compact position. A noun or pronoun can be used between "coil" and "up." The snake coiled itself up and began hissing at us. Coil up that hose when you're done with it.
coil (itself) up
[for something] to wrap or roll itself into a coil. The snake coiled itself up, trying to hide. It coiled up, ready to strike.
coil something up
to roll or twist something into a coil. Maria coiled the strip of stamps up and put them in the little dispenser. Please coil up the rope.