1610s, "to wind, gather into rings one above the other" (trans.), from French coillir "to gather, pick," from Latin colligere "to gather together" from assimilated form of com "together" (see co-) + legere "to gather," from PIE root *leg- (1) "to collect, gather." Intransitive sense "to form rings or spirals" is by 1798. Related: Coiled; coiling.
1620s, "length of rope or cable," a specialized nautical sense from coil (v.). General sense "ring or series of rings in which a pliant body is wound" is from 1660s; hence, such a form forced onto a non-pliant body (1826). Specific sense "electrical conductor wound in a coil" is from 1849. Related: Coils.