The word coil comes from the Middle English word collen, which means to wind or twist. The Middle English word coilen is thought to come from the Old English word cwelan, which also means to wind or twist.  Another possibility is that it comes from Old French coillir, from Latin colligere ‘gather together’. 

The first recorded use of "coil" as a noun, meaning "a winding or rolling together," is from 1567.  The first recorded use of "coil" as a verb, meaning "to wind or gather (ropes, hair, etc) into loops or (of rope, hair, etc) to be formed in such loops," is from 1611. 

Examples of coil (noun) used in a sentence:  
"A thick coil of smoke rose from the chimney". 
"The mechanic replaced the old ignition coil with a new one". 
"She wore a coil of beads around her neck". 
"The snake coiled around the branch, ready to strike". 
"The steel arrives at the factory in coils". 
"The coil of wire was used to create a magnetic field"

Examples of coil (verb) used in a sentence:  
"The snake coiled tightly around the branch." 
"She coiled the loose thread around her finger."
"Please coil the rope and hang it on the hook."
"The cat coiled up into a ball on the rug."
"A long scarf was coiled around her neck."
"I want you to coil the garden hose and store it away."
"She coiled her hair into a neat bun."

Just the facts:

COIL Definition & Meaning - Merriam-Webster

There is also the term coiled spring which carries with it not only the idea of the spring being a coil of metal but also there being tension that is ready to be be released, often explosively.

A person can be referred to as being like a coiled spring because they will be quick to get pissed off, tell you off or respond aggressively. In other words, that they are ready to do something at any moment and without hesitation.